JEE Main - Fundamental integrals involving algebraic trigonometric exponential and logarithmic functions Online Test (MCQ Quiz)

1. What is the integral of x^n with respect to x, where n is not equal to -1?

A) n x^(n-1) B) x^(n+1) / (n+1) C) log(x) D) e^x

2. What is the integral of 1/x with respect to x?

A) x B) log(x) C) log|x| D) 1/x^2

3. What is the integral of e^x with respect to x?

A) e^x B) e^(x+1) C) x e^x D) log(e^x)

4. What is the integral of a^x with respect to x, where a > 0 and a != 1?

A) a^x B) a^x / log(a) C) a^x * log(a) D) x a^(x-1)

5. What is the integral of sin(x) with respect to x?

A) cos(x) B) -cos(x) C) tan(x) D) sec(x)

6. What is the integral of cos(x) with respect to x?

A) sin(x) B) -sin(x) C) cot(x) D) csc(x)

7. What is the integral of sec^2(x) with respect to x?

A) tan(x) B) cot(x) C) sec(x) D) csc(x)

8. What is the integral of csc^2(x) with respect to x?

A) cot(x) B) -cot(x) C) tan(x) D) -tan(x)

9. What is the integral of sec(x)tan(x) with respect to x?

A) sec(x) B) -sec(x) C) tan(x) D) -tan(x)

10. What is the integral of csc(x)cot(x) with respect to x?

A) csc(x) B) -csc(x) C) cot(x) D) -cot(x)

11. What is the integral of 1/sqrt(1-x^2) with respect to x?

A) arcsin(x) B) arccos(x) C) arctan(x) D) arcsec(x)

12. What is the integral of 1/(1+x^2) with respect to x?

A) arcsin(x) B) arccos(x) C) arctan(x) D) arcsec(x)

13. What is the integral of k f(x) dx, where k is a constant?

A) k f(x) B) f(x) / k C) k integral f(x) dx D) integral k dx

14. What is the integral of [f(x) + g(x)] dx?

A) integral f(x) dx + g(x) B) f(x) + integral g(x) dx C) integral f(x) dx + integral g(x) dx D) integral [f(x)g(x)] dx

15. What is the integral of [f(x) - g(x)] dx?

A) integral f(x) dx - g(x) B) f(x) - integral g(x) dx C) integral f(x) dx - integral g(x) dx D) integral [f(x)/g(x)] dx

16. Evaluate the integral of 2x^3 dx.

A) x^4 / 2 B) x^4 C) 2x^4 D) x^3

17. Evaluate the integral of (3x^2 + 2x + 1) dx.

A) x^3 + x^2 + x B) 3x^3 + x^2 + x C) x^3 + 2x^2 + x D) x^3 + x^2 + x + C

18. Evaluate the integral of (e^x + sin(x)) dx.

A) e^x + cos(x) B) e^x - cos(x) C) e^x + sin(x) D) e^x - sin(x)

19. Evaluate the integral of (1/x + 5) dx.

A) log|x| + 5x B) log|x| + 5 C) x + 5x D) log(x) + 5x

20. Evaluate the integral of (sec^2(x) - 1) dx.

A) tan(x) - x B) tan(x) + x C) sec(x) - x D) tan(x)

21. Evaluate the integral of (2^x + x^2) dx.

A) 2^x / log(2) + x^3 / 3 B) 2^x * log(2) + x^3 / 3 C) 2^x + x^3 / 3 D) 2^x / log(2) + x^2

22. What is the integral of cos(2x) dx?

A) sin(2x) B) sin(2x) / 2 C) -sin(2x) / 2 D) 2sin(2x)

23. What is the integral of sin(3x) dx?

A) cos(3x) / 3 B) -cos(3x) / 3 C) 3cos(3x) D) -3cos(3x)

24. What is the integral of e^(kx) dx, where k is a non-zero constant?

A) e^(kx) B) k e^(kx) C) e^(kx) / k D) e^(kx) * k

25. What is the integral of 1/(ax+b) dx, where a is non-zero?

A) log|ax+b| B) (1/a) log|ax+b| C) a log|ax+b| D) log(ax+b)

26. What is the integral of (1+x)^n dx, where n is not equal to -1?

A) (1+x)^(n+1) B) (1+x)^(n+1) / (n+1) C) n(1+x)^(n-1) D) (1+x)^n

27. What is the integral of (ax+b)^n dx, where n is not equal to -1 and a is non-zero?

A) a(ax+b)^(n+1) / (n+1) B) (ax+b)^(n+1) / (n+1) C) (ax+b)^(n+1) / (a(n+1)) D) n(ax+b)^(n-1)

28. Evaluate the integral of (x+1)^2 dx.

A) (x+1)^3 B) (x+1)^3 / 3 C) 2(x+1) D) x^2/2 + x

29. Evaluate the integral of (2x+1)^3 dx.

A) (2x+1)^4 / 4 B) (2x+1)^4 / 8 C) 3(2x+1)^2 D) 2(2x+1)^4

30. What is the integral of tan(x) dx?

A) sec^2(x) B) -sec(x) C) log|sec(x)| D) log|cos(x)|

31. What is the integral of cot(x) dx?

A) -csc^2(x) B) csc(x) C) log|sin(x)| D) log|csc(x)|

32. What is the integral of sec(x) dx?

A) tan(x) B) sec(x)tan(x) C) log|sec(x) + tan(x)| D) log|sec(x) - tan(x)|

33. What is the integral of csc(x) dx?

A) -cot(x) B) -csc(x)cot(x) C) log|csc(x) - cot(x)| D) log|csc(x) + cot(x)|

34. Evaluate the integral of (e^(2x) + cos(3x)) dx.

A) 2e^(2x) + 3sin(3x) B) e^(2x)/2 + sin(3x)/3 C) e^(2x) + sin(3x) D) e^(2x)/2 + cos(3x)/3

35. Evaluate the integral of (x^2 + 1/x + e^x) dx.

A) x^3/3 + log|x| + e^x B) 2x + 1/x^2 + e^x C) x^3/3 + log|x| + e^x + C D) x^3/3 + log(x) + e^x

36. What is the integral of 1/sqrt(a^2 - x^2) dx, where a > 0?

A) (1/a) arcsin(x/a) B) arcsin(x/a) C) arcsin(ax) D) a arcsin(x)

37. What is the integral of 1/(a^2 + x^2) dx, where a > 0?

A) (1/a) arctan(x/a) B) arctan(x/a) C) arctan(ax) D) a arctan(x)

38. Evaluate the integral of (3x^2 + 2/x + e^x) dx.

A) x^3 + 2log|x| + e^x B) 6x + 2/x^2 + e^x C) x^3 + 2log|x| + e^x + C D) x^3 + log|x^2| + e^x

39. Evaluate the integral of (cos(x) - sec^2(x)) dx.

A) sin(x) - tan(x) B) sin(x) + tan(x) C) -sin(x) - tan(x) D) sin(x) - cot(x)

40. Evaluate the integral of (4x^3 - 3/x) dx.

A) x^4 - 3log|x| B) 12x^2 - 3/x^2 C) x^4 - 3log|x| + C D) 4x^4 - 3log|x|

41. What is the integral of (a^x - x^a) dx, where a > 0 and a != 1?

A) a^x / log(a) - x^(a+1) / (a+1) B) a^x * log(a) - (a+1)x^a C) a^x / log(a) - (a+1)x^a D) a^x - x^(a+1) / (a+1)

42. Evaluate the integral of (1/sqrt(x) + 2x) dx.

A) 2sqrt(x) + x^2 B) sqrt(x) + x^2 C) 1/(2sqrt(x)) + 2 D) 2sqrt(x) + x^2 + C

43. What is the integral of (1 - cos(x)) dx?

A) x - sin(x) B) x + sin(x) C) -sin(x) - cos(x) D) x - cos(x)

44. What is the integral of (1 + sin(x)) dx?

A) x - cos(x) B) x + cos(x) C) sin(x) - cos(x) D) x - sin(x)

45. Evaluate the integral of (e^x + 1/x) dx.

A) e^x + log(x) B) e^x + log|x| C) e^x + 1/x^2 D) e^x + log|x| + C

46. Evaluate the integral of (2x + cos(x)) dx.

A) x^2 + sin(x) B) 2 + sin(x) C) x^2 + sin(x) + C D) x^2 - sin(x)

47. What is the integral of 1/cos^2(x) dx?

A) tan(x) B) -cot(x) C) sec(x) D) sin(x)

48. What is the integral of 1/sin^2(x) dx?

A) cot(x) B) -cot(x) C) tan(x) D) -tan(x)

49. Evaluate the integral of (x^n + a^n) dx, where n is a constant and a is a constant.

A) x^(n+1)/(n+1) + a^n x B) (n+1)x^n + a^n x C) x^(n+1)/(n+1) + x a^n D) x^(n+1)/(n+1) + a^(n+1)/(n+1)

50. Evaluate the integral of (sin(x) + cos(x)) dx.

A) -cos(x) + sin(x) B) cos(x) + sin(x) C) -cos(x) + sin(x) + C D) sin(x) - cos(x)

Fundamental integrals involving algebraic trigonometric exponential and logarithmic functions - Online Test

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