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Antidifferentiation Practice Questions

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Updated on Oct 1, 2011

To review these concepts, go to Antidifferentiation Study Guide.

Antidifferentiation Practice Questions

Evaluate the following integrals.

  1. x5dx
  2. x12dx
  3. u6du
  4. x2dx
  5. xdx
  6. t–3dt
  7. t5dt
  8. 3xdx
  9. 3udu
  10. 5dx
  11. 5dt
  12. 8dx

Evaluate the following integrals.

  1. 9x4 dx
  2. 8u2 du
  3. (x – √x)dx
  4. (6x2 – 10x + 5) dx
  5. 12x3 dx
  6. (3x2 + 4)dx
  7. (6x – 4) dx
  8. (3t11 + 9t2 + t) dt
  9. (1 – t2) dt
  10. (8x3 + 10x2 – 4x + 2) dx
  11. (10u4 – 4u + 1) du
  12. 12√xdx
  13. dx
  14. dx

Evaluate the following integrals.

  1. (x2 – 5cos(x)) dx
  2. (3ex + 2x3) dx
  3. du
  4. (θ + 2sin(θ)) dθ
  5. (sin(x) + 2ex) dx
  6. (x + ex) dx
  7. 1e dx

Solutions

  1. x6 + c
  2. x13 + c
  3. u7 + c
  4. 72
  5. 40
  6. t–2 + c = – + c
  7. x + c
  8. x + c
  9. u + c
  10. 5x + c
  11. 5t + c
  12. 40
  13. x5 + c
  14. u3 + c
  15. x2x + c
  16. 2x3 – 5x2 + 5x + c
  17. 48
  18. 11
  19. 115
  20. t12 + 3t3 + t2 + c
  21. –6
  22. 2x4 + x3 – 2x2 + 2x + c
  23. 58
  24. 208
  25. + c
  26. x3 – 5sin(x) + c
  27. 3ex + x4 + c
  28. ln|ul| + c
  29. θ2 – 2cos(θ) + c
  30. –cos(x) + 2ex + c
  31. ( + e1) – (0 + e0) = e
  32. 4ln(e) – 4ln(1) = 4 – 0 = 4
  33. 4√2
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