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REVIEW TEST 4

REVIEW TEST 4. 1. Find the following integral. A. x 8 + c. B. x 8 /8 + c. D. x 6 /6 + c. C. 7 x 6 + c. E. None of the above. Sorry, that answer is incorrect. Remember the power rule for integration –. Please click here to try again.

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REVIEW TEST 4

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  1. REVIEWTEST 4

  2. 1. Find the following integral A. x 8 + c B. x 8 /8 + c D. x 6 /6 + c C. 7 x 6 + c E. None of the above

  3. Sorry, that answer is incorrect. Remember the power rule for integration – Please click here to try again.

  4. Great, the correct answer is x 8 /8 + c, by substituting the power 7 into the power rule. Please click here for the next question.

  5. 2. Find the following integral A. x –3 /- 3 + c B. x –1 /- 3 + c D. - 2x –3 + c C. - x – 1 + c E. None of the above

  6. Not quite, that answer is incorrect. Remember the power rule for integration – Please click here to try again.

  7. Hey great, the correct answer is - x – 1 + c, by substituting the power - 2 into the power rule. Please click here for the next question.

  8. 3. Find the following integral A. B. D. C. E. None of the above

  9. Too bad, that answer is incorrect. Remember the power rule for integration – Please click here to try again.

  10. OK, the correct answer is Using the power rule twice; once with n = 3 and again with n = - 3. Please click here for the next question.

  11. 4. Ready to step it up a notch? A. e x + c B. x e x + c D. 2e 2x + c C. E. None of the above

  12. Not quite, that answer is incorrect. Remember the rule for exponential functions for integration – Please click here to try again.

  13. Terrrrriffffic, the correct answer is e x + c, Using the rule for exponential expressions for integration. Please click here for the next question.

  14. 5. Find the following integral A. ln x + c B. e x + c D. x + c C. E. None of the above

  15. Not quite, that answer is incorrect. Remember the rule for logarithmic functions for integration – Please click here to try again.

  16. Terrrrriffffic, the correct answer is ln x + c, since Please click here for the next question.

  17. 6. Now, let’s try something really interesting. A. B. ln x – ex + c C. 3ln x – 3ex + c D. E. None of the above

  18. That answer is incorrect. It is a hard one! You must use both the rule for exponential functions for integration and the rule for logarithmic functions for integration as in the previous two problems. Please click here to try again.

  19. Terrrrriffffic, the correct answer is 3ln x – 3ex + csince Please click here for the next question.

  20. Let’s go back to the power rule. A. B. D. C. E. None of the above

  21. That answer is incorrect. Try changing the radical to exponential form! Then use the power rule. Please click here to try again.

  22. Grrrrreat, the correct answer is And using the power rule for integration yields - Please click here for the next question.

  23. 8. Find the following integral A. -2 x -1 / 2 + c • 2 x 1 / 2 + c C. -2 x 1 / 2 + c D. 2 x -1 / 2 + c E. None of the above

  24. That answer is incorrect. Try changing the radical to exponential form! Then use the power rule. Please click here to try again.

  25. WOW, the correct answer is indeed 2x ½ + c. Please click here for the next question.

  26. 9. Let’s complete that idea. A. 2x 2/3 + 3x 3/2 + c • -6x -1/2 + 3x -4/3 + c C. 2x 3/2 + 3x 2/3 + c D. -2x 3/2 - 3x - 2/3 + c E. None of the above

  27. That answer is incorrect. That answer is incorrect. Try changing the radicals to exponential form! See the previous two problems. Please click here to try again.

  28. Great, the correct answer is 2x 3/2 + 3x 2/3 + c, since Please click here for the next question.

  29. 10. OK. Let’s try some involving substitution techniques. A. D. C. E. None of the above

  30. No that answer is incorrect. Try substitution. Let u = x 5 – 3 and find du and make an adjustment to x 4 that is appropriate. Please click here to try again.

  31. Yes! Yes! Yes!, the correct answer is by letting u = x 5 – 3 and finding du = 5x 4 dx The problem then needs adjusting by multiplying and dividing by 5. Please click here for the next question.

  32. 11. A. B. 5 (2x 5 – 4x + 7) 4 (20x 3 ) + c C. D. E. None of the above

  33. That answer is incorrect. You must substitute correctly! Let u = 2x 5 – 4x + 7, then du = 10x 4 – 4 which is 2 (5x 4 – 2) . SO the original problem becomes Please click here to try again.

  34. Grrrrreat, the correct answer is Let u = 2x 5 – 4x + 7, then du = 10x 4 – 4 which is 2 (5x 4 – 2) . SO the original problem becomes Please click here for the next question.

  35. 12. A. 2 (x 2 – 3) - ½ + c B. 5 (x 2 – 3) -1/2 + c C. 2 (x 2 – 3) – 1/2 + c D. 5 (x 2 – 3) ½ + c E. None of the above

  36. Too bad that answer is incorrect. First, rewrite the problem - Let u = x 2 – 3, then du = 2xdxwhich means that we need a factor of 2 in the problem or Please click here to try again.

  37. Yes, you are an integrating machine. First, rewrite the problem Let u = x 2 – 3, then du = 2xdxwhich means that we need a factor of 2 in the problem or Please click here for the next question.

  38. 13. A. C. D. E. None of the above

  39. No that answer is incorrect. You must substitute correctly! Let u = 2x 3 , then du = 6x 2 dx . Please click here to try again.

  40. Correctamundo, the answer is Let u = 2x 3 , then du = 6x 2 dx , then Please click here for the next question.

  41. 14. A. 2 (2x – 1) + c • ½ (2x – 1) + c C. ½ ln | 2x – 1| + c D. 2x – 1 + c E. None of the above

  42. No that answer is incorrect. No that answer is incorrect. You must substitute correctly! Let u = 2x - 1 , then du = 2 dx . Please click here to try again.

  43. Yes, the answer is ½ ln | 2x – 1| + c Let u = 2x - 1 , then du = 2 dx , then, Please click here for the next question.

  44. Now that you have indefinite integrals down cold let’s try some definite integrals. A. 5 • 6.67 C. – 8.67 D. 8.67 E. None of the above

  45. Too bad that answer is incorrect. • To find the definite integral you have two options- • Calculate the indefinite integral and evaluate at the top limit (3) and subtract the value at the bottom limit (1) • OR • 2. Use your calculator to do the work. Use the “Calc” menu and integrate. Please click here to try again.

  46. Yes, the answer is 8.67 I used the “Calc” menu and “integrate”. Please click here for the next question.

  47. 16. A. 3 • 5.17 C. 2.02 D. - 3.5 E. None of the above

  48. Too bad that answer is incorrect. • To find the definite integral you have two options- • Calculate the indefinite integral and evaluate at the top limit (3) and subtract the value at the bottom limit (1) • OR • 2. Use your calculator to do the work. Use the “Calc” menu and integrate. Please click here to try again.

  49. Yes, the answer is 2.02 I used the “Calc” menu and “integrate”. Please click here for the next question.

  50. 17. A. 3 • 5.17 C. 27.23 D. - 3.5 E. None of the above

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