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Mathematics - Definite Integration

Practise 116 NTA Abhyas (JEE Main) questions on Definite Integration. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Definite Integration has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 116 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. 1The value of the integral = 0 sin x + cos x d x , (where . denotes the greatest integer function) is equal to
  2. 2If ∫ 20 40 sin ⁡ x sin ⁡ x + s i n 60 - x d x = k , then the value of k 4 is equal to
  3. 3Consider 1 = 4 2 e sin x + 1 e cos x + 1 d x and 2 = 4 2 e cos x + 1 e sin x + 1 d x , then
  4. 4The value of I = ∫ - 1 1 x sin ⁡ ( π x ) d x is (where [·] denotes the greatest integer function)
  5. 5Consider I = ∫ 0 1 d x 1 + x 5 . Then, I satisfies
  6. 6lf f x = sin lim t → 0 2 x π cot − 1 x t 2 , then ∫ - π 2 π 2 f x d x is equal to (where, x ≠ 0 )
  7. 7If the integral I = 0 sec - 1 sec x 1 + tan 8 x d x , x 2 , then the value of I is equal to (where is the greatest integer function)
  8. 8Given f x = x | x | for x ≤ - 1 x + 1 + 1 - x for - 1 x 1 - x | x | for x ≥ 1 , where [.] denotes the greatest integer function. If I = ∫ -
  9. 9The value of ∫ - 1 1 c o t - 1 x + x 3 + x 5 x 4 + x 2 + 1 d x is equal to
  10. 10If the value of the integral I = 0 2 s g n e x d x is equal to k , then the smallest prime number greater than 2 k is (where, s g n x repres
  11. 11A continuous function f x is such that f 3 x = 2 f x , ∀ x ∈ R . If ∫ 0 1 f x d x = 1 , then ∫ 1 3 f x d x is equal to
  12. 12The value of ∫ 0 π 3 l o g 1 + 3 tan ⁡ x d x is equal to
  13. 13Let the function F be defined as F x = 1 x e t t dt , x 0 , then the value of the integral 1 x e t t + a dt , where a 0 , is
  14. 14If I n = 0 2 2 d x 1 - x n , then the value of lim n I n is equal to
  15. 15If f k - x + f x = sin ⁡ x, then the value of integral Ι = ∫ 0 k f x d x is equal to
  16. 16The value of the integral 0 4 x 2 x 2 - 4 x + 8 d x is equal to
  17. 17The value of the integral ∫ − a a e x 1 + e x d x is
  18. 18The value of Ι = l i m n → ∞ ∑ r = n 2 n n r 2 is equal to
  19. 19Let Ι 1 = ∫ 0 1 ln ⁡ x x 2 + 4 x + 1 d x and Ι 2 = ∫ 1 ∞ ln ⁡ x x 2 + 4 x + 1 d x , then
  20. 20If f 0 = 0 , f 3 = 3 and f ′ 3 = 4 , then the value of ∫ 0 1 x f ″ 3 x d x is equal to
  21. 21For x ∈ R , x ≠ 0 , if y x is a differentiable function such that x ∫ 1 x y t d t = x + 1 ∫ 1 x t y t d t , then y x equals (where C is a co
  22. 22If I 1 = 0 2 e sin x 1 + x cos x d x and I 2 = 0 2 e cos x 1 - x sin x d x , then I 1 I 2 is equal to (where x denotes the greatest integer
  23. 23The value of the integral ∫ - 3 π 3 π s i n 3 x d x is equal to
  24. 24Consider the integral I n = ∫ 0 π 4 sin 2 n − 1 x sin x d x , then the value of I 20 - I 19 is
  25. 25The value of the integral = 0 d x 1 + x 2020 1 + x 2 is equal to k , then the value of 16 k is equal to
  26. 26If the definite integral I = 0 sin x d x = = 0 n a sin . (where, is the greatest integer function), then the value of a n + n is equal to
  27. 27If g x is a differentiable function such that ∫ 1 sin ⁡ α x 2 g x d x = sin ⁡ α - 1 , ∀ α ∈ 0 , π 2 , then the value of g 1 3 is equal to
  28. 28Consider the integral A = 0 1 e x - 1 x d x and B = 0 1 x e x - 1 d x . Then, which of the following is incorrect?
  29. 29If ∫ 0 1 x 11 e - x 24 d x = A , and ∫ 0 1 x 3 e - x 8 d x = B, then the relation between A and B is
  30. 30If I 1 = ∫ 0 2 π sin 3 ⁡ x d x and I 2 = ∫ 0 1 ln ⁡ 1 x - 1 d x , then
  31. 31If the integral I n = ∫ 0 π 2 sin ⁡ 2 n - 1 x sin ⁡ x d x , then the value of I 20 3 - I 19 3 is
  32. 32If f x satisfies f x + f 3 - x = 3 ∀ x ∈ R , then the value of integral I = ∫ 3 4 9 4 f f x d x is equal to
  33. 33The value of ∫ π 6 π 3 e sec 2 ⁡ x sin ⁡ x cos 3 ⁡ x d x is equal to
  34. 34Let I = ∫ 0 1 sin ⁡ x x d x a n d J = ∫ 0 1 cos ⁡ x x d x . Then, which one of the following is true?
  35. 35The integral I = ∫ e e + 1 1 + x 2 1 + x 3 d x satisfies
  36. 36The integral ∫ − 1 / 2 1 / 2 ( [ x ] + ℓ n ( 1 + x 1 − x ) ) d x is equal to ( x is the greatest integer ≤ x )
  37. 37Consider A = ∫ 0 π 4 s i n 2 x x d x , then
  38. 38The value of ∫ 0 π 2 cos ⁡ 2 x cos 2 2 ⁡ x cos 2 3 ⁡ x cos ⁡ 2 4 x d x is equal to
  39. 39Let Ι 1 = ∫ 1 π 2 d t 1 + t 6 and Ι 2 = ∫ 0 π 2 x cos ⁡ x d x 1 + x s i n x + cos ⁡ x 6 , then
  40. 40If f x is a continuous function and x 2 x 4 t 3 f t d t = s i n 2 x , then f 1 is equal to
  41. 41If a = 0 1 c o s sin x sec x d x , then the value of a 2 + c o s 2 sin 1 is equal to
  42. 42If 0 1 e x 2 x - a d x = 0 , then the value of 0 1 e x 2 d x is equal to
  43. 43If f 1 + x = f 1 - x x R , then the value of the integral = - 7 9 f x f x + f 2 - x d x is
  44. 44The value of ∫ - π π s i n y 1 + t a n 2 y d y (where [ x ] is greatest integer function) is
  45. 45If ∫ 0 π / 4 [ tan x + cot x ] d x = π m , then the value of m is equal to
  46. 46The value of ∫ π 2 π [ 2 sin x ] d x is equal to (where [.] represents the greatest integer function)
  47. 47The value of the integral ∫ - 4 4 e x x d x is equal to (where . denotes the fractional part function)
  48. 48The value of the integral I = ∫ 0 π 2 sin 3 ⁡ x - cos 3 ⁡ x 1 + sin 6 ⁡ x cos 6 ⁡ x d x is equal to
  49. 49The limit L = lim n → ∞ ⁡ ∑ r = 4 n - 4 n n 2 + r 2 satisfies the relation
  50. 50The value of the integral Ι = ∫ 0 100 π d x 1 + e sin ⁡ x is equal to

Frequently Asked Questions

1.How many questions are available for Definite Integration?

This chapter includes 116 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 Definite Integration 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 Definite Integration questions in NTA Abhyas (JEE Main)?

Of the 116 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Definite Integration should I focus on?

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