JEE Main - Areas under simple curves and regions bounded by curves Online Test (MCQ Quiz)

1. What is the area of the region bounded by the curve y = x^2, the x-axis, and the lines x = 1 and x = 3?

A) 26/3 B) 10/3 C) 8/3 D) 4/3

2. Find the area of the ellipse x^2/a^2 + y^2/b^2 = 1.

A) πab B) 2πab C) πa^2b D) πab^2

3. What is the area of the region bounded by the curve y = sin(x), the x-axis, and the lines x = 0 and x = π?

A) 0 B) 1 C) 2 D) π

4. Calculate the area of the region enclosed by the parabola y^2 = 4ax and the line y = mx.

A) 2a^2m^3 / 3 B) 4a^2m^3 / 3 C) 2a^2 / (3m^2) D) 4a^2 / (3m^2)

5. Find the area of the region bounded by the curve y = x^3, the x-axis, and the lines x = -1 and x = 1.

A) 0 B) 1/4 C) 1/2 D) 1

6. What is the area of the region bounded by the curve y = e^x, the x-axis, and the lines x = 0 and x = 1?

A) e - 1 B) e C) e + 1 D) 1

7. Determine the area of the region bounded by the curve y = 1/x, the x-axis, and the lines x = 1 and x = 2.

A) ln(2) B) ln(1) C) ln(3) D) ln(4)

8. Find the area of the region bounded by the circle x^2 + y^2 = r^2.

A) πr^2 B) 2πr^2 C) πr D) 2πr

9. What is the area of the region bounded by the curve y = sqrt(a^2 - x^2) and the x-axis from x = 0 to x = a?

A) πa^2/4 B) πa^2/2 C) πa^2 D) a^2

10. Calculate the area of the region bounded by the curve y = x^2 and the line y = x.

A) 1/6 B) 1/4 C) 1/3 D) 1/2

11. Find the area of the region bounded by the curve y = |x| and the line y = 2.

A) 2 B) 4 C) 6 D) 8

12. What is the area of the region bounded by y = sin(x) and y = cos(x) between x = 0 and x = π/4?

A) sqrt(2) - 1 B) 2 - sqrt(2) C) sqrt(2) D) 1

13. Determine the area of the region bounded by the curve y = x^2 - 4 and the x-axis.

A) 16/3 B) 32/3 C) 8/3 D) 4/3

14. Find the area of the region bounded by the curves y = x^2 and y = 2x - x^2.

A) 1/3 B) 1/2 C) 2/3 D) 1

15. What is the area of the region bounded by the hyperbola x^2/a^2 - y^2/b^2 = 1 and its latus rectum?

A) ab/2 B) ab C) 2ab D) ab^2

16. Calculate the area of the region bounded by the curve y = x^4 and the line y = 1.

A) 2/5 B) 4/5 C) 1/5 D) 3/5

17. Find the area of the region bounded by the curve y = x(x-1)(x-2) and the x-axis.

A) 0 B) 1/2 C) 1 D) 3/2

18. What is the area of the region bounded by the curve y = tan(x), the x-axis, and the lines x = 0 and x = π/4?

A) ln(2) B) ln(sqrt(2)) C) ln(1/2) D) 1

19. Determine the area of the region enclosed by the cardioid r = a(1 + cos(θ)).

A) 3πa^2/2 B) πa^2 C) 2πa^2 D) 3πa^2

20. Find the area of the region bounded by the curve y = x^2 and the tangent line at x = 1.

A) 1/3 B) 1/2 C) 2/3 D) 1

21. What is the area of the region bounded by the curve y = 1/(1+x^2) and the x-axis from x = -∞ to x = ∞?

A) π/2 B) π C) 2π D) 1

22. Calculate the area of the region bounded by the curve y = x^3 - x and the x-axis.

A) 0 B) 1/4 C) 1/2 D) 1

23. Find the area of the region bounded by the curve y = sqrt(x), the x-axis, and the line x = 4.

A) 8/3 B) 16/3 C) 4/3 D) 32/3

24. What is the area of the region bounded by the curve y = x^2 and the line y = 4?

A) 16/3 B) 32/3 C) 8/3 D) 4/3

25. Determine the area of the region bounded by the curve y = 1/sqrt(1-x^2) and the x-axis from x = 0 to x = 1.

A) π/2 B) π C) 1 D) ln(2)

26. Find the area of the region bounded by the curve y = x^2 and the line x = y^2.

A) 1/3 B) 1/2 C) 2/3 D) 1

27. What is the area of the region bounded by the curve y = sec^2(x), the x-axis, and the lines x = 0 and x = π/4?

A) 1 B) sqrt(2) C) 2 D) ln(2)

28. Calculate the area of the region bounded by the curve y = x^3 and the line y = x.

A) 0 B) 1/4 C) 1/2 D) 1

29. Find the area of the region bounded by the curve y = |x - 1| and the x-axis from x = 0 to x = 2.

A) 1 B) 2 C) 3 D) 4

30. What is the area of the region bounded by the curve y = 1/x^2, the x-axis, and the lines x = 1 and x = 2?

A) 1/2 B) 1 C) 3/2 D) 2

31. Determine the area of the region bounded by the curve y = x^2 and its normal at x = 1.

A) 1/3 B) 1/2 C) 2/3 D) 1

32. Find the area of the region bounded by the curve y = x^2 and the line y = x + 2.

A) 4/3 B) 9/2 C) 16/3 D) 27/4

33. What is the area of the region bounded by the curve y = sqrt(a^2 - x^2)?

A) πa^2 B) πa^2/2 C) πa^2/4 D) 2πa^2

34. Calculate the area of the region bounded by the curve y = x^2 - 2x and the x-axis.

A) 4/3 B) 2/3 C) 8/3 D) 1/3

35. Find the area of the region bounded by the curve y = x^2 and the line y = 2 - x^2.

A) 4/3 B) 2/3 C) 8/3 D) 1

36. What is the area of the region bounded by the curve y = 1/x, the x-axis, and the lines x = e and x = e^2?

A) 1 B) 2 C) ln(2) D) e

37. Determine the area of the region bounded by the curve y = x^2 and the line y = -x + 2.

A) 9/2 B) 16/3 C) 27/4 D) 4/3

38. Find the area of the region bounded by the curve y = x^2 and the line y = 4x - 3.

A) 1/3 B) 1/2 C) 2/3 D) 1

39. What is the area of the region bounded by the curve y = x^2 and the line y = 4x?

A) 16/3 B) 32/3 C) 8/3 D) 4/3

40. Calculate the area of the region bounded by the curve y = x^2 and the line y = 8 - x^2.

A) 32/3 B) 16/3 C) 64/3 D) 4/3

41. Find the area of the region bounded by the curve y = x^2 and the line y = 3x - 2.

A) 1/6 B) 1/3 C) 1/2 D) 2/3

42. What is the area of the region bounded by the curve y = x^2 and the line y = 3x.

A) 9/2 B) 27/4 C) 16/3 D) 4/3

43. Determine the area of the region bounded by the curve y = x^2 and the line y = 6 - x^2.

A) 16/3 B) 32/3 C) 64/3 D) 4/3

44. Find the area of the region bounded by the curve y = x^2 and the line y = 5x - 4.

A) 1/6 B) 1/3 C) 1/2 D) 2/3

45. What is the area of the region bounded by the curve y = x^2 and the line y = 5x.

A) 125/6 B) 25/2 C) 10/3 D) 5/3

46. Calculate the area of the region bounded by the curve y = x^2 and the line y = 7 - x^2.

A) 64/3 B) 32/3 C) 128/3 D) 4/3

47. Find the area of the region bounded by the curve y = x^2 and the line y = 7x - 6.

A) 125/6 B) 1/3 C) 1/2 D) 2/3

48. What is the area of the region bounded by the curve y = x^2 and the line y = 7x.

A) 343/6 B) 49/2 C) 7/3 D) 343/3

49. Determine the area of the region bounded by the curve y = x^2 and the line y = 9 - x^2.

A) 128/3 B) 64/3 C) 256/3 D) 8/3

50. Find the area of the region bounded by the curve y = x^2 and the line y = 9x - 8.

A) 343/6 B) 1/6 C) 1/2 D) 2/3

Areas under simple curves and regions bounded by curves - Online Test

Test Results