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Cengage Maths Solutions Class 12 Integrals - Calculus

Cengage Maths Solutions Class 12 Integrals PDfs provides accurate solutions to practice before your final exam. Students can study this comprehensive Cengage Maths PDf Solutions on Integrals and its various sub-topics for effective exam preparation. The Cengage 12 PDF solutions help the student to swiftly practice and revise the important concepts just before the annual exam to score high marks in maths.<br>For more such video solutions/Pdf solution, visit https://doubtnut.com and clear your doubt instantly.

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Cengage Maths Solutions Class 12 Integrals - Calculus

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  1. CENGAGE / G TEWANI MATHS SOLUTIONS CHAPTER INTEGRALS || CALCULUS  Download Doubtnut Today Ques No. Question CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration (1 + x)3 Evaluate: ∫ dx. 1 √x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration ∫2x+1− 5x−1 10x Evaluate 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate: ∫sec2xcosec2xdx. 3  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 1 − cosx Evaluate ∫ dx. 4 1 + cosx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 1 Evaluate: ∫ dx 5 1 + sinx  Watch Free Video Solution on Doubtnut

  2. CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 1 − cos2x ∫tan−1{√( )} Evaluate: 6 1 + cos2x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration secx Evaluate: ∫ dx. 7 secx + tanx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration ∫(secx + tanx)2dx Evaluate: 8  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate : ∫(1 − cosx)cosec2xdx 9  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate: ∫amxbnxdx 10  Watch Free Video Solution on Doubtnut

  3. CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration tanx Evaluate: 11 dx secx + tanx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration x4 1 If ∫ dx = f(x) + c, the ≠ valuate∫ dx. 12 x + x5 x + x5  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration (x3+ 8)(x − 1) If ∫ 13 dx x2− 2x + 4  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration sin3x + cos3x Evaluate: ∫ dx 14 sin2xcos2x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 15 Evaluate: `inttan^(-1)(secx+tanx)dx ,-pi/2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 16 + 2

  4. x + 2 Evaluate: ∫ dx. (x + 1)2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 8x + 13 Evaluate ∫ dx 17 √4x + 7  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate ∫sin3xdx 18  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate ∫sin2xsin3xdx. 19  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration dx Evaluate: ∫ 20 (2x − 7)√(x − 3)(x − 4)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration

  5. 1 21 Evaluate: ∫ dx. √3x + 4 − √3x + 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration dx x Find the values of such that ∫ = tan( + a) + b aandb 22 1 + sinx 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 3 x2− 1 1 2 Evaluate: ∫(x + ) ( )dx 23 x2 x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration x Evaluate: ∫ dx 24 √x + 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration sec2x Evaluate: ∫ 25 dx 3 + tanx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration −x x−

  6. ex− e−x Evaluate: ∫ 26 dx ex+ e−x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 1 − tanx Evaluate: ∫ dx 27 1 + tanx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 1 Evaluate: ∫ dx. 28 1 + e−x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration sin2x Evaluate: ∫ dx. 29 a2sin2x + b2cos2x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration tanx log( ) 2 Evaluate: ∫ 30 dx sinx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration

  7. √2 + logx 31 Evaluate: ∫ dx x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate: ∫tan4xdx 32  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate: ∫(tanx − x)tan2xdx 33  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 3 (sin−1x) Evaluate: ∫ 34 dx √1 − x2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration x + 1 )(x + logx)2dx Evaluate: ∫( 35 x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration

  8. 36 √tanx Evaluate: ∫ dx. sinxcosx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration cotx Evaluate: ∫ dx 37 √sinx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration dx Evaluate: ∫ 38 3 x2(x4+ 1) 4  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration dx Evaluate: ∫ 39 √2ax − x2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions e3x+ e5x Evaluate: ∫ dx 40 ex+ e−x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫tan2xsin2xdx 41  Watch Free Video Solution on Doubtnut

  9. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By SubstitutionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions cosx − sinx Evaluate: ∫ (2 + 2sin2x)dx 42 cosx + sinx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫cosec4xdx 43  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions sin2x Evaluate: ∫ 44 (a + b cosx)2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫sinxcosxcos2xcos4xcos8xdx 45  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions (1 + 1nx)5 Evaluate: ∫ 46 dx x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

  10. cos2x − cos2θ 47 Evaluate: ∫ dx cosx − cosθ  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x3 Evaluate: ∫ dx 48 x + 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 49 √x + √x − 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫(1 + 2x + 3x2+ 4x3+ )dx, ( < |x| < 1) 50  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1n(1nx) Evaluate: ∫ dx, (x > 0) 51 x1nx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

  11. dx Evaluate: ∫ 52 x + xlogx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫secpxtanxdx 53  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions ∫sin6x cos8x Evaluate: 54  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫sin2xd(tanx) 55  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1

  12. 1 Evaluate: ∫ dx 56 √3sinx + cosx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 57 sin(x − a)sin(x − b)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫{1 + 2tanx(tanx + secx)) dx 2 58  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 1 59 (1 + sinx) 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 60 cosx − sinx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

  13. sinx 61 Evaluate: ∫ dx sin(x − a)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫tan3xdx 62  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫sin(ex)d(ex) 63  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫cos3x√s ∈ dx 64  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions sin2x Evaluate : ∫ dx 65 a2+ b2sin2x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

  14. 66 ∫(222x (22x)(2x))dx Evaluate:  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 67 1 1 x + x 2 3  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions e2x− 1 Evaluate: ∫ dx. 68 e2x+ 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 2x −√sin−1x Evaluate: ∫ dx. √1 − x2 69  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions e√xcos(e√x) Evaluate: ∫ 70 dx √x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions tanx Evaluate: ∫ dx 71 a + btan2x  Watch Free Video Solution on Doubtnut

  15. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By SubstitutionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions ex(1 + x) Find ∫ dx 72 cos2(xe2)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions sin3xdx Evaluate: ∫ 73 (cos4x + 3cos2x + 1)tan−1(secx + cosx)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 74 (x2+ 2x + 2)2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x x)1nxdx. e x Evaluate: ∫(( ) + ( ) 75 x e  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ 76 √e5x(e2x+ e− 2x)34  Watch Free Video Solution on Doubtnut

  16. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By SubstitutionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 77 Find: ∫sin5xdx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Find: ∫sin3xcos5xdx 78  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Find: ∫ 79 sinxcos3x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫sin2xcos2xdx 80  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x2tan−1x3 Evaluate: ∫ dx 81 1 + x6  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

  17. ∫√xdx 1 + x 82 Evaluate:  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions cotx Evaluate: ∫ dx 83 √sinx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 84 x +√x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 85 9 + 16sin2x  Watch Free Video Solution on Doubtnut

  18. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By SubstitutionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions e2x− 2ex Evaluate: ∫ dx 86 e2x+ 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions ax3+ bx Evaluate: ∫ dx 87 x4+ c2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 88 2 2 x (1 + x ) 3 3  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions −1dx Evaluate: ∫e3logx(x4+ 1) 89  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions ∫secxdx √cos2x Evaluate: 90  Watch Free Video Solution on Doubtnut

  19. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By SubstitutionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫sin3xcos2xdx 91  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions xdx Evaluate: ∫ 92 √1 + x2+√(1 + x2)3  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 2x + 1 Evaluate: ∫ dx 93 x4+ 2x3+ x2− 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 94 x2− x + 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 95 2x2+ x − 1  Watch Free Video Solution on Doubtnut

  20. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By SubstitutionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions cosx Evaluate: ∫ dx 96 sin(x − )sin(x + ) π π 6 6  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions sinx Evaluate: ∫ dx. 97 sin3x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 98 3 + sin2x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 99 1 + sinx + cosx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 3sinx + 2cosx Evaluate: ∫ dx 100 3cosx + 2sinx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x2+ 1 Evaluate: ∫ dx 101 x4+ 1  Watch Free Video Solution on Doubtnut

  21. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By SubstitutionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x2+ 4 Evaluate: ∫ dx 102 x4+ 16  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫√tanθdthη 103  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x2− 1 Evaluate: ∫ 104 (x2+ 1)√1 + x4  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 105 2x2+ x − 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x Evaluate: ∫ dx 106 x4+ x2+ 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

  22. x2− 1 Evaluate: ∫ 107 dx 1 (x4+ 3x2+ 1)tan−1(x + ) x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 108 x4+ 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 109 sin4x + cos4x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 110 x2√1 + x2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 111 3 (a2+ x2) 2  Watch Free Video Solution on Doubtnut

  23. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By SubstitutionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 112 √(x − 1)(x − 2)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions sec2x Evaluate: ∫ dx 113 √tan2x + 4  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions The number of irrational roots of the equation 4x 5x 3 is c. d. 1 114 + = − a.4 b. 0 2 x2+ x + 3 x2− 5x + 3 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

  24. ex 115 Evaluate: ∫ dx e2x+ 6ex+ 5  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 4x + 1 Evaluate: ∫ 116 x2+ 3x + 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 + x Evaluate: ∫√ dx. 117 x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x2 Evaluate: ∫ dx 118 √1 − x6  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x Evaluate: ∫√ dx 119 a3− x3  Watch Free Video Solution on Doubtnut

  25. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By SubstitutionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: 120 dx √1 − e2x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 2x + 3 Evaluate: ∫ dx 121 √x2+ 4x + 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 5 x 2 Evaluate: ∫ dx 122 √1 + x7  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫x3d(tan−1x) 123  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts Evaluate: ∫xsin3xdx. 124  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts Evaluate: ∫xlogxdx. 125  Watch Free Video Solution on Doubtnut

  26. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts Evaluate: ∫sin−1xdx. 126  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts x − sinx Evaluate: ∫ dx 127 1 − cosx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts Evaluate is polynomaial function of then the degree, prove that ∫f(x) ∫exf(x)dx = ex[f(x)f'(x) + fx= fx+ ...... 128 + ( − 1)nfn(x)] fn(x)dx +dnf where dxn  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts x Evaluate: ∫sin−1√ dx. 129 a + x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation cosx Evaluate: − logxsinx)dx. ∫( 130 x

  27.  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation 1 ∫(log(logx) + )dx Evaluate: 131 (logx)2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫ex(f(x) + f′(x))dx = exf(x) + C 132  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation 1 1 Evaluate: ∫ex( )dx. − 133 x2 x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation exx Evaluate: ∫ dx 134 (x + 1)2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation 1 − sinx Evaluate: ∫ex( )dx 135 1 − cosx

  28.  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫{sin(logx) + cos(logx)}dx 136  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation logx Evaluate: ∫ dx 137 (1 + logx)2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation ∫esin−1xdx. Evaluate: 138  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫xsin2xdx 139  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation

  29. 140 Evaluate: if ∫f(x)dx = g(x),then∫f−1(x)dx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: if ∫g(x)dx = g(x), then∫g(x){f(x) + f′(x)}dx 141  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫cos√xdx 142  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation xsin−1x Evaluate: ∫ dx 143 √1 − x2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫tan−1√xdx 144  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation

  30. 145 x Evaluate: ∫cosxlog(tan )dx 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation 2 logx − 1 ∫( ) Evalaute: dx 146 1 + (logx)2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation ex(2 − x2)dx Evaluate: ∫ 147 (1 − x)√1 − x2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫ex(1 + tanx + tan2x)dx 148  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫sin2(logx)dx 149  Watch Free Video Solution on Doubtnut

  31. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫[f(x)gx− fxg(x)]dx 150  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation 1 − x Evaluate: ∫tan−1√ dx 151 1 + x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 2x − 1 Evaluate: ∫ dx 152 (x − 1)(x + 2)(x − 3)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 2x Evaluate: ∫ dx 153 (x2+ 1)(x2+ 2)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 1 Evaluate: ∫ dx 154 sinx − sin2x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 1 − cosx Evaluate: ∫ 155 cosx(1 + cosx)dx  Watch Free Video Solution on Doubtnut

  32. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial FunctionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions (x − 1)(x − 2)(x − 3) Evaluate: ∫ dx 156 (x − 4)(x − 5)(x − 6)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions x2+ 1 Evaluate: ∫ dx 157 (x − 1)2(x + 3)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions x Evaluate: ∫ dx 158 (x − 1)(x2+ 4)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions sinx Evaluate: ∫ dx 159 sin4x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions logexe ⋅ loge2xe ⋅ loge3xe Evaluate: ∫ dx x 160  Watch Free Video Solution on Doubtnut

  33. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial FunctionsCENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 1 Evaluate: ∫ dx 161 (x2− 4)√x + 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions x2+ 1 Evaluate: ∫ dx 162 x(x2− 1)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 1 Evaluate: ∫ dx 163 x4− 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions If the product of positive numbers is n . Then their sum is nn 164  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions dx Evaluate: ∫ 165 sinx(3 + cos2x)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions

  34. cos2xsin4xdx Evaluate: ∫ 166 cos4x(1 + cos22x)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 167 Evaluate: ∫√x2+ 2x + 5dx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 168 Evaluate: ∫√1 + 3x − x2dx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 169 Evaluate: ∫(x − 5)√x2+ xdx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 170 (x − 3)√x + 1dx  Watch Free Video Solution on Doubtnut

  35. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 171 dx (x + 1)√x2− 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 172 dx (1 − x2)√1 + x2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 173 dx (x + 1)√x2− 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational Evaluate: ∫sec3xdx 174  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational + 1

  36. x + 1 175 Evaluate: ∫ dx (x − 1)√x + 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational x Evaluate: ∫ 176 dx (x2+ 4)√x2+ 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 177 dx (x + 1)√x2+ x + 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational x3+ 1 178 Evaluate: ∫ dx x2+ x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 −dx 2 179 Evaluate: Evaluate: ∫x−11(1 + x4)  Watch Free Video Solution on Doubtnut

  37. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 (x − x3) 3 180 Evaluate: ∫ dx x4  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ dx 181 1 [(x − 1)3(x + 2)5] 4  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational √tanx 182 Evaluate: ∫ dx sinxcosx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational dx Evaluate: ∫ 183 3√sin11xcosx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational sinx 184 Evaluate: ∫ dx 2 + sin2x  Watch Free Video Solution on Doubtnut

  38. CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational dx Evaluate: ∫ 185 4 x2(1 + x5) 5  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 186 dx 3 x2(x4+ 1) 4  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ (x4− x) 4 187 Evaluate: ∫ dx x5  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational x + 1 Evaluate: ∫ 188 dx (x − 1)√x + 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational

  39. 189 Evaluate: ∫xx1n(ex)dx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational dx Evaluate: ∫ (x − p)√(x − p)(x − q) 190  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational n [√1 + x2+ x] 191 Evaluate: ∫ dx √1 + x2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational dx Evaluate: ∫ 192 cos3x√sin2x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 193

  40. Evaluate: ∫sec5xcosec3xdx  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration b Evaluate: using limit of sum exdx ∫ 194 a  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration b Evaluate: using limit of sum sinxdx ∫ 195 a  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 2 Evaluate the definite integrals as limit of sums x2dx ∫ 196 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration b dx Evaluate ∫ ,wherea,b > 0. 197 √x a  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 1 1

  41. 198 1 1 1 Evaluate lim n→ ∞n[ ] + + + 6n2 (n + 1)(n + 2) (n + 2)(n + 4)  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 1 1 1 Evaluate: lim n→ ∞[ ] + + + + 199 na + 1 na + 2 na nb  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 ((n + 1)(n + 2)...(n + n)) n Evaluate: 200 lim n→ ∞ n  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration (12+ 22+ 33+ + n2)(13+ 23+ 33+ + n3) Evaluate: (lim)n− → 201 ∞ 16+ 26+ 36+ + n6  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration b Evaluate: ∫ cosxdx 202 a  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration b Evaluate: x3dx ∫ 203 a  Watch Free Video Solution on Doubtnut

  42. CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 1 1 ∞( ) Evaluate: (lim)n− → + + + 204 √4n2− 1 √4n2− 22 √3n2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration sec21 sec24 1 1 Evaluate: + 2/n2 sec21] ∞[ (lim)n− → + + 205 n2 n2 n2 n  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration n k Evaluate ∑ (lim)n− → 206 ∞ n2+ k2 k=1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 ∑r = 1n√r∑r = 1n √r Evaluate: 207 (lim)n− → ∞ ∑r = 1nr  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1/n n! Evaluate: (lim)n→ ∞[ ] 208 nn  Watch Free Video Solution on Doubtnut

  43. CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 0 dx Evaluate: ∫ 209 x2+ 2x + 2 −1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 1 If then find the value of f(x) = min (|x|,1 − |x|, )∀x ∈ R, ∫ f(x)dx. 210 4 − 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration π dx Find the mistake of the following evaluation of the integral I = ∫ 1 + 2sin2x 0 π dx I = ∫ 211 cos2x + 3sin2x sec2xdx 0 π 1 [tan−1(√3tanx)]π0 = 0 = ∫ = 1 + 3tan2x √3 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration tan−11 1 d Find the value of ( )dx ∫ 212 dx x −1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration Let be a continuous function on f Prove that there exists a number [a,b]. x ∈ [a, b]

  44. 213 x b such that ∫ f(t)dx = ∫ f(t)dt. a x  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 e−xdx If , then find the value of k. ∫ = (log)e(1 + e) + k 214 1 + ex 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration A continuous real function satisfies f 1 2 . f(2x) = 3(f(x)∀x ∈ R 215 then find the value of If∫ ∫ f(x)dx = 1, f(x)dx 0 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 F ∈ dthevalueof∫ logxdx. 216 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1

  45. 1 217 If ,then find the value of xf' '(2x)dx f(0) = 1,f(2) = 3,f′(2) = 5 ∫ 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 2π dx x Consider the integral making the substitution we ∫ tan( ) = t, 5 − 2cosx 2 0 2π 0 2dt dx have The result is I = ∫ = ∫ = 0 218 5 − 2cosx 1−t2 (1 + t2)[5 − 2 ] 0 0 1+t2 obviously wrong, since the integrand is positive and consequently the integral of this function cannot be equal to zero. Find the mistake.  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration π dx Evaluate: ∫ 219 1 + sinx 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration ∞ −1dx Evaluate: (ex+1+ e3−x) ∫ 220 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 sin−1x √2 Evaluate: ∫ dx 221 (1 − x2)√1 − x2 0  Watch Free Video Solution on Doubtnut

  46. CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 2 − x2 Evaluate: ∫ dx 222 (1 + x)√1 − x2 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration π dx 2 Evaluate: ∫ 223 a2cos2x + b2sin2x 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration π 2 Let: Then find the value of (1 − sint)nsin2tdt an= ∫ lim n→ ∞nan 224 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 102 1 1 (x − 1)(x − 2). .(x − 100) × ( ∫ + + x − 1 x − 2 0 225 .1 )dx = 101! − 100! . x − 100  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 2 Evaluate: ∣∣x3− x∣∣dx. ∫ 226 −1

  47.  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 2π Evaluate: sin− 1(sinx)dx ∫ 227 π − 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 1 1 Evaluate: sin−1(2x√1 − x2)dx. ∫ 228 √1 − x2 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals π 2 Evaluate: √cosx − cos3xdx ∫ 229 π − 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals b |x| Show that ∫ dx = |b| − |a|. 230 x a  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals x Let: Then discuss continuity and differentiability of |2t − 3|dt. f(x) = ∫ 0 3

  48. 231 f(x)atx =3 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals If denotes the greatest integer less than or equal to 2 x2[x]dx. then find the value of the [x] x, 232 integral ∫ 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 2 Evaluate: denotos the greatest integer function. [x2− x + 1]dx, where[.] ∫ 233 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 5π 12 Evaluate: , where denotes the greatest integer function. ∫ [tanx]dx [.] 234 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 10π Evaluate: represents greatest integer function. [tan−1x]dx,where[x] ∫ 235 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals ∞

  49. ∞ Evaluate: represents greatest integer function. [2e−x]dx, where[x] ∫ 236 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 2π Evaluate: ,where denotes the greatest integer function. [.] ∫ [sinx]dx 237 0  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 5 1 Evaluate: denotes the greatest integer function). x2[x + ]dx(where[.] ∫ 238 2 −5  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals π 2 Evaluate: ∫ |sinx − cosx|dx 239 0  Watch Free Video Solution on Doubtnut

  50. CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite IntegralsCENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 4 4 Evaluate: then find the value of ∫ f(x)dx = 4and∫ (3 − f(x))dx = 7, 240 −1 2 −1 ∫ f(x)dx. 2  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 3 x2+ 1 x Evaluate: (tan−1( ) + tan−1( ))dx ∫ 241 x2+ 1 x −1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals a .a− [ (log)ax]dx,(a > 1). Evaluate: ∫ x 242 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals e6 logx Evaluate: denotes the greatest integer function. ]dx,where[.] [ ∫ 243 3 1  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 1 Find the value of denote the greatest function [x2+ {x}]dx, where[.]and{.} ∫ 244 −1 and fractional parts of respectively. x,  Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 2π Evaluate: , where denotes the greatest integer function [cot−1]dx ∫ [.] 245 π 2  Watch Free Video Solution on Doubtnut

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