Jump to a section

Mathematics - Area Under Curves

Practise 90 NTA Abhyas (JEE Main) questions on Area Under Curves. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Area Under Curves has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 90 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1Let f x = x 2 + 4 : x 0 4 - 2 x : x 0 , then the area bounded by y = f x and the x -axis from x = - 1 to x = 3 is equal to
  2. 2If the area bounded by the curves x 2 + y 2 ≤ 4 , x + y ≥ 2 , and y ≥ 1 is 2 π K - K 2 - 1 2 sq. units, then the value of K is equal to
  3. 3The parabolas y 2 = 4 x and x 2 = 4 y divide the square region bounded by the lines x = 4 , y = 4 and the coordinate axes. If S 1 , S 2 , S
  4. 4The area (in sq. units) bounded by y = x x and the line y = x is equal to
  5. 5The area (in sq. units) bounded by the curve y = m a x. x 3 , x 4 and the x -axis from x = 0 to x = 1 is
  6. 6The area bounded by y = f x , x = 1 , x = 4 and the x -axis is 12 square units where f x is a differentiable function such that f 1 = 3 and
  7. 7The area (in sq. units) bounded by x 2 + y 2 = 1 and the curve y 2 ≥ x 2 , above the x -axis is
  8. 8The area bounded by y = max ⁡ x 2 , x 4 , y = 1 and the y -axis from x = 0 to x = 1 is
  9. 9The area (in sq. units) of the region bounded by the curves y = 2 - x 2 and y = x is k , then the value of 3 k is
  10. 10If the area covered by y = 2 x and y = 2 2 x - 1 from x = 1 to x = e is ln a sq. units, then 2 e - 1 2 a 2 is equal to
  11. 11Let f x be a continuous and positive function and the area bounded by y = f x , the x -axis and the lines x = 0 and x = a is 4 a 3 + sin a s
  12. 12The area bounded by the curve y = x 2 x - 1 2 with the x -axis is k sq. units, then the value of 60 k is equal to
  13. 13If the maximum area bounded by y 2 = 4 x and the line y = m x m 1 , 3 is k square units, then the smallest prime number greater than 3 k is
  14. 14The area (in sq. units) bounded by y = 1 x and y = 1 2 x - 1 between x = 1 and x = 2 is
  15. 15The area (in square units) bounded by y = x 2 + x + 1 and x + y = 2 is
  16. 16If the area bounded by y = x 2 and y = 2 1 + x 2 is K 1 - K 2 3 sq. units (where K 1 , K 2 Z ), then the value of K 1 + K 2 is equal to
  17. 17If the area bounded by f x = tan 3 ⁡ x + tan ⁡ x from x = 0 to x = π 4 is k square units, then the maximum value of g x = k sin ⁡ x is ∀ x ∈
  18. 18The area (in sq. units) bounded by x + y = 2 with the co-ordinate axes is equal to (where, . denotes the greatest integer function)
  19. 19The area bounded by the curves y = cos x and y = sin 2 x , x 6 , 2 is equal to
  20. 20The area between the curves x = 4 y - y 2 and x = 0 is square units, then the value of 3 is equal to
  21. 21The area enclosed between the curves y = ax 2 and x = ay 2 a 0 is 1 sq unit. If the value of a is 3 3 λ , then the value of λ is
  22. 22The area bounded by the parabola 4 y = 3 x 2 , the line 2 y = 3 x + 12 and the y -axis is
  23. 23The area (in sq. units) bounded by y = 2 x and y = 2 x - x 2 from x = 1 to x = 2 is k log 2 e - l , then the value of k l is equal to
  24. 24The area (in sq. units) bounded by y = 2 - x - 2 and the x -axis is
  25. 25The area (in sq. units) bounded by y = ln ⁡ x , y = x e and the y -axis is equal to
  26. 26The area (in sq. units) of the region { x , y : y 2 ≥ 2 x and x 2 + y 2 ≤ 4 x , x ≥ 0 , y ≥ 0 } is
  27. 27The area bounded by f x = sin ⁡ 2 x x ≥ 0 cos ⁡ 2 x x 0 with the x -axis, x = - π 4 and x = π 4 is k square units. Then, the value of 4 k is
  28. 28The area bounded by y = x - 1 with the x -axis from x = 0 to x = 1 is k square units, then 4 k is equal to
  29. 29The area (in sq. units) covered by x - y = - 3 with the coordinate axes is (where, is the greatest integer function)
  30. 30The area bounded by y = 1 - x 2 and y = x 3 - x is divided by y -axis in the ratio λ : 1 ∀ λ 1 , then λ is equal to
  31. 31The area (in sq. units) bounded by the curve y = x : x ∈ 0,1 2 - x : x ∈ 1,2 with the x -axis from x = 0 to x = 2 is
  32. 32If the area bounded by y + x - π ≤ π and y ≥ π 2 is K π 2 sq. units, then the value of 8 K is equal to
  33. 33The area (in sq. units) bounded by the curve e x y - 2 = 0 with the x -axis from x = 0 to x = ln ⁡ 2 is
  34. 34The area (in sq. units) bounded by x + y = 2 in the first and third quadrant is (where, . is the greatest integer function),
  35. 35The area bounded by y = ( x 2 - x ) 2 with the x -axis, between its two relative minima, is A sq. units. Then, the value of 15 A is equal to
  36. 36The area (in sq. units) bounded by y = e x : x 0 e - x : x 0 with the x -axis from x = - 1 to x = 1 is
  37. 37If the area bounded by the curves x 2 + y 2 and y x is k 2 sq. units, then 2 k is equal to
  38. 38The area of the region (in square units) above the x -axis bounded by the curve y ⁡ = tan x , 0 ≤ x ⁡ ≤ π 2 and the tangent to the curve at
  39. 39The area bounded by the graph y = x - 3 , above the x -axis from x = - 2 to x = 3 is ( . denotes the greatest integer function)
  40. 40Consider f x = minimum x + 2 , 4 - x , ∀ x ≤ 4 . If the area bounded by y = f x and the x -axis is 22 k square units, then the value of k is
  41. 41The area (in sq. units) bounded between the curves y = e x cos ⁡ x and y = e x sin ⁡ x from x = π 4 to x = π 2 is
  42. 42The area bounded by the curves y = ln x , y = ln x , y = ln x and y = ln x , for x ( 1 , 1 ) is
  43. 43The area between the curve y = 2 x 4 - x 2 , the x -axis and the ordinates of the two minima of the curve is
  44. 44If the area enclosed by y 2 = 2 x and x 2 + 4 + 4 x = 4 y 2 is k square units, then the value of 3 k is equal to
  45. 45If the area bounded by y 2 = 4 a x and x 2 = 4 a y is 64 3 square units, then the positive value of a is
  46. 46If f x is a non-negative function such that the area bounded by y = f x , x -axis and the lines x = 0 and x = α is 4 α sin ⁡ α + 2 sq. units
  47. 47The value of the parameter ‘a' such that the area bounded by y = a 2 x 2 + a x + 1 , coordinate axes and the line x = 1 attains its least va
  48. 48The area (in sq. units) bounded by the curve f x = e - x x ≥ 1 x - 1 + 1 e x 1 and the x -axis is
  49. 49If the area bounded by the curve y + x 2 = 8 x and the line y = 12 is K sq. units, then the value of 3 K 10 is
  50. 50The area of the closed region bounded by y = sec - 1 ⁡ x , y = c o s e c - 1 x and the line x - 1 = 0 is

Frequently Asked Questions

1.How many questions are available for Area Under Curves?

This chapter includes 90 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

These are NTA Abhyas (JEE Main) questions specifically for the Area Under Curves chapter. Questions from other exams like JEE Main or JEE Advanced are organised separately under their respective exam sections.

3.What is the difficulty level of Area Under Curves questions in NTA Abhyas (JEE Main)?

Of the 90 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Area Under Curves should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.