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Integration

Integration. Jami Wang Period 3 EC PPT. Integration – the Antiderivative. C represents Constant Raise the power Guess. Check. Answer. Ex: ∫ 2X dx Guess: X 2 Check: 2X Answer : X 2 + C Off by a constant = good Off by a variable = new guess.

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Integration

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  1. Integration Jami Wang Period 3 EC PPT

  2. Integration – the Antiderivative • C represents Constant • Raise the power • Guess. Check. Answer. • Ex: ∫ 2X dx • Guess: X2 • Check: 2X • Answer : X2 + C • Off by a constant = good • Off by a variable = new guess

  3. Integration – the Antiderivative (continued) • When power raised = zero, use ln • Ex: ∫ 2/X dx( ∫ 2X-1dx ) • Guess: 2lnX • Check: (2) 1/x • Answer: 2lnx + Cor lnX2 + C

  4. Most Complicated Rule • Start out with the complicated part and ignore the easy part • Can’t decide the most complicated one – choose one • Ex: ∫ X (X2- 1)9 • Guess: 1/20(X2- 1)10 • Check: 10 (X2- 1)9 (2X) • Answer: 1/20 (X2- 1)10 + C

  5. Most Complicated Rule (continued) • Ex2: ∫ (ln x6 / x) dx • Guess: 1/7 (lnx)7 • Check: (lnx) 6 (1/x) • Answer: 1/7 (lnx) 7+ C

  6. Definite Integrals • Ex: 30∫ √ (y+1) dy3∫0 √ (y+1)1/2dy • Guess: 2/3 (y+1)3/2 • Check: 3/2 (y+1)1/2 • substitution then subtraction • Biggest number goes first 2/3 (y+1)3/2 30 = 2/3 (4)3/2 – 2/3 (1) 3/2*use x values to find y values • Answer: 14/3

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