Definite Integrals – 50 items Problem Set Homework

Note: Latest Update in May 2025

Now that you have learned the Definite Integration Formulas it’s time to solve some exercises. Always remember that the best way to fully understand every concept in math is through practice solving problems. If you are ready, get a pen and paper and give your best shot. You can finish these exercises in about 2 hours. Good luck.

Definite Integrals Problems

1. ∫(from 0 to 1) 3x^2 dx

2. ∫(from 1 to 2) (4x^3 + 2x) dx

3. ∫(from 0 to 3) (5x^4 – 3x^2 + 1) dx

4. ∫(from 1 to 4) x^(1/2) dx

5. ∫(from 2 to 3) x^(-2) dx

6. ∫(from 0 to 1) (x^(3/2) + x^(1/2)) dx

7. ∫(from 1 to e) (1/x) dx

8. ∫(from 0 to 1) e^x dx

9. ∫(from 0 to 2) 2e^x dx

10. ∫(from 0 to 1) (e^x + x) dx

11. ∫(from 0 to π/2) sin(x) dx

12. ∫(from 0 to π) cos(x) dx

13. ∫(from 0 to π/4) (sin(x) + cos(x)) dx

14. ∫(from 0 to π/2) 3sin(x) dx

15. ∫(from 0 to π) 4cos(x) dx

16. ∫(from 0 to π/4) sec^2(x) dx

17. ∫(from π/4 to π/2) csc^2(x) dx

18. ∫(from 0 to π/3) sec(x)tan(x) dx

19. ∫(from π/6 to π/2) csc(x)cot(x) dx

20. ∫(from 0 to π/4) (sec^2(x) + csc^2(x)) dx

21. ∫(from 1 to 3) 5 dx

22. ∫(from 0 to 2) (2x + 3) dx

23. ∫(from -1 to 2) (x^2 – 4x + 7) dx

24. ∫(from 0 to 8) x^(1/3) dx

25. ∫(from 1 to 2) x^(-3) dx

26. ∫(from 0 to 1) (x^(2/3) + x^(4/3)) dx

27. ∫(from 1 to 2) (1/(2x)) dx

28. ∫(from 0 to 1) 3e^(2x) dx

29. ∫(from 0 to 1) (e^(3x) – 2x) dx

30. ∫(from 0 to π/4) 2sin(2x) dx

31. ∫(from 0 to π/6) 3cos(3x) dx

32. ∫(from 0 to π/2) (sin(4x) – cos(5x)) dx

33. ∫(from 0 to 1) x*sin(x^2) dx

34. ∫(from 0 to 1) x*e^(x^2) dx

35. ∫(from 0 to 2) (x / (x^2 + 1)) dx

36. ∫(from 0 to π/4) tan(x) dx

37. ∫(from π/4 to π/2) cot(x) dx

38. ∫(from 0 to π/3) sec(x) dx

39. ∫(from π/6 to π/2) csc(x) dx

40. ∫(from 0 to π) sin^2(x) dx

41. ∫(from 0 to π) cos^2(x) dx

42. ∫(from 0 to π/4) tan^2(x) dx

43. ∫(from π/4 to π/2) cot^2(x) dx

44. ∫(from 0 to π) x*cos(x) dx

45. ∫(from 0 to 1) x*e^x dx

46. ∫(from 1 to e) ln(x) dx

47. ∫(from 1 to 2) x*ln(x) dx

48. ∫(from 0 to π/2) e^(2x)*sin(x) dx

49. ∫(from 0 to π) e^x*cos(2x) dx

50. ∫(from 2 tо 3) 1/(x^2 – 1) dx

Are you Done? I know you are confident enough with your answers. Check the answers key to know if you got a perfect score.

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