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Mathematics - Definite Integration

Practise 52 JEE Advanced previous year questions on Definite Integration, compiled from papers spanning 2006 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Advanced tests.

Definite Integration has been asked in 21 of the 27 years of JEE Advanced papers analysed (2000–2026), with 52 questions in all. 21% of them were easy, 46% moderate and 33% tough. Most of its questions came from 2015, with 7 questions that year. In the last three years (2024–2026) it had 4 questions across 6 papers, about 0.7 per paper.

The chapter's 8 topics are not weighted equally: Properties of Definite Integration (22 questions, 42%), Leibnitz Rule of Differentiation (7 questions, 13%), and Definite Integration by Parts (6 questions, 12%) have been asked the most. Properties of Definite Integration has also led over the last five years, with 5 questions. Properties of Definite Integration has produced the most tough questions (7).

  1. 1The value of the definite integral is2026 (Paper 2)Properties of Definite Integration
  2. 2If then the value of is ____________. (Here, the inverse trigonometric function assumes values in .)2025 (Paper 2)Properties of Definite Integration
  3. 3Paragraph: Let \(f: [0, { }{2} ] [0,1]\) be the function defined by \(f(x)= ^2 x\) and let \(g: [0, { }{2} ] [0, )\) be the function defined2024 (Paper 2)Properties of Definite Integration
  4. 4Let \(f: [0, { }{2} ] [0,1]\) be the function defined by \(f(x)= ^2 x\) and let \(g: [0, { }{2} ] [0, )\) be the function defined by \(g(x)=2024 (Paper 2)Properties of Definite Integration
  5. 5For x , let tan - 1 x - 2 , 2 . Then the minimum value of the function f : defined by f x = 0 x tan - 1 x e t - cos t 1 + t 2023 d t is2023 (Paper 2)Leibnitz Rule of Differentiation
  6. 6Consider the equation 1 e log e x 1 2 x a - log e x 3 2 2 d x = 1 , a - , 0 1 , . Which of the following statements is/are TRUE?2022 (Paper 1)Definite Integration by Substitution
  7. 7The greatest integer less than or equal to 1 2 log 2 x 3 + 1 d x + 1 log 2 9 2 x - 1 1 3 d x is2022 (Paper 2)Properties of Definite Integration
  8. 8For positive integer n , define f n = n + 16 + 5 n - 3 n 2 4 n + 3 n 2 + 32 + n - 3 n 2 8 n + 3 n 2 + 48 - 3 n - 3 n 2 12 n + 3 n 2 + + 25 n2022 (Paper 2)Definite as Limit of Sum
  9. 9Let f : - 2 , 2 be a continuous function such that f 0 = 1 and 0 3 f t d t = 0 Then which of the following statements is (are) TRUE?2021 (Paper 2)Leibnitz Rule of Differentiation
  10. 10Let , and be functions such that and , for all Define The value of 16 S 1 is ___.2021 (Paper 2)Properties of Definite Integration
  11. 11Let , and be functions such that and , for all Define The value of 48 S 2 2 is ____.2021 (Paper 2)Properties of Definite Integration
  12. 12For any real number x , let x denotes the largest integer less than or equal to x . If I = 0 10 10 x x + 1 d x , then the value of 9 I is __2021 (Paper 2)Properties of Definite Integration
  13. 13Which of the following inequalities is/are TRUE?2020 (Paper 1)Properties Involving Inequalities
  14. 14Let f : be a differentiable function such that its derivative f is continuous and f = - 6 . If F : 0 , is defined by F x = 0 x f t d t , and2020 (Paper 2)Definite Integration by Parts
  15. 15If I = 2 - 4 4 d x 1 + e s i n x 2 - c o s 2 x then find 27 I 2 equals____2019 (Paper 1)Properties of Definite Integration
  16. 16The value of the integral 0 / 2 3 cos cos + sin 5 d equals2019 (Paper 2)Properties of Definite Integration
  17. 17Let f : R R a n d g : R R be two non-constant differentiable functions. If f x = e f x - g x g x f o r a l l x R , and f 1 = g 2 = 1 then wh2018 (Paper 1)Properties of Definite Integration
  18. 18The value of the integral 0 1 2 1 + 3 x + 1 2 1 - x 6 1 4 d x is2018 (Paper 2)Definite Integration by Substitution
  19. 19Let f : R R be a differentiable function such that f 0 = 0 , f 2 = 3 and f 0 = 1 . If g x = x 2 f t c o s e c t - cot t c o s e c t f t d t 2017 (Paper 1)Properties of Definite Integration
  20. 20The value of I = k = 1 98 k k + 1 k + 1 x ( x + 1 ) d x , then2017 (Paper 2)Properties Involving Inequalities
  21. 21If g x = sin x sin 2 x sin - 1 t d t , then2017 (Paper 2)Leibnitz Rule of Differentiation
  22. 22The value of - 2 2 x 2 cos x 1 + e x d x is equal to2016 (Paper 2)Properties of Definite Integration
  23. 23Let f : R R be a function defined by f x = x , x 2 0 , x 2 , where [ x ] is the greatest integer less than or equal to x . If I = - 1 2 x f 2015 (Paper 1)Properties of Definite Integration
  24. 24Let F x = x x 2 + 6 2 cos 2 t d t for all x R a n d f : 0 , 1 2 0 , be a continuous function. For a 0 , 1 2 , if F a + 2 is the area of the 2015 (Paper 1)Leibnitz Rule of Differentiation
  25. 25If = 0 1 e 9 x + 3 tan - 1 x 12 + 9 x 2 1 + x 2 d x where tan - 1 x takes only principal values, then the value of log e 1 + - 3 4 is2015 (Paper 2)Definite Integration by Substitution
  26. 26The option(s) with the value of a and L that satisfy the following equation is(are) 0 4 e t sin 6 a t + cos 4 a t d t 0 sin 6 a t + cos 4 a 2015 (Paper 2)Properties of Definite Integration
  27. 27Let f x = 7 tan 8 x + 7 tan 6 x - 3 tan 4 x - 3 tan 2 x for all x - 2 , 2 . Then the correct expression(S) is(are)2015 (Paper 2)Definite Integration by Parts
  28. 28Let f x = 192 x 3 2 + sin 4 x for all x R with f 1 2 = 0 . If m 1 2 1 f x d x M , then the possible values of m and M are2015 (Paper 2)Properties Involving Inequalities
  29. 29Let F : R R be a thrice differentiable function. Suppose that F 1 = 0 , F 3 = - 4 and F x 0 all x 1 2 , 3 . Let f x = x F ( x ) for all x R 2015 (Paper 2)Definite Integration by Parts
  30. 30The value of 0 1 4 x 3 d 2 d x 2 1 - x 2 5 d x is ____________2014 (Paper 1)Definite Integration by Parts
  31. 31The following integral 4 2 2 c o s e c x 17 d x is equal to2014 (Paper 2)Definite Integration by Substitution
  32. 32Paragraph: Given that for each , exists. Let this limit be . In addition, it is given that the function is differentiable on . Question: The2014 (Paper 2)Properties of Definite Integration
  33. 33Paragraph: Given that for each , exists. Let this limit be . In addition, it is given that the function is differentiable on . Question: The2014 (Paper 2)Properties of Definite Integration
  34. 34Match the following. List I List II (A) The number of polynomials f(x) with non negative integer coefficients of degree 2 , satisfying f(0) 2014 (Paper 2)Properties of Definite Integration
  35. 35For a R (the set of all real numbers), a - 1 , lim n 1 a + 2 a + + n a n + 1 a - 1 na + 1 + na + 2 + + na + n = 1 6 0 Then a =2013 (Paper 2)Definite as Limit of Sum
  36. 36The value of the integral is2012 (Paper 2)Properties of Definite Integration
  37. 37The value of is2011 (Paper 1)Properties of Definite Integration
  38. 38Let be a differentiable function such that . If for all , then the value of is2011 (Paper 1)Leibnitz Rule of Differentiation
  39. 39Let be a continuous function such that for all . Let and be the area of the region bounded by and the -axis. Then,2011 (Paper 2)Definite Integration by Parts
  40. 40Preview not available - open to view this question.2011 (Paper 2)Miscellaneous
  41. 41The value(s) of is (are)2010 (Paper 1)Miscellaneous
  42. 42For any real number , let denotes the largest integer less than or equal to . Let be a real valued function defined on the interval by . The2010 (Paper 1)Properties of Periodic Functions
  43. 43Let be a non-negative function defined on the interval . If2009 (Paper 1)Leibnitz Rule of Differentiation
  44. 44Preview not available - open to view this question.2009 (Paper 1)Miscellaneous
  45. 45If , , then2009 (Paper 2)Properties of Definite Integration
  46. 46Let be a continuous function, which satisfies . Then, the value of is2009 (Paper 2)Leibnitz Rule of Differentiation
  47. 47Let and , for , then2008 (Paper 1)Definite as Limit of Sum
  48. 48Paragraph: Consider the functions defined implicitly by the equation on various intervals in the real line. If , the equation implicitly def2008 (Paper 1)Miscellaneous
  49. 49Match the integrals in Column I with the values in Column II.2007 (Paper 1)Definite Integration by Substitution
  50. 50Paragraph: Read the following passage and answer the questions. For every function which is twice differentiable, these will be good approxi2006Miscellaneous

Frequently Asked Questions

1.How many questions are available for Definite Integration?

This chapter includes 52 questions compiled from JEE Advanced papers spanning 2006 to 2026.

2.Are these questions only from JEE Advanced, or from other exams too?

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

3.Is Definite Integration an important chapter for JEE Advanced Mathematics?

Definite Integration has appeared in 21 of the 21 years of JEE Advanced papers covered here, with 52 questions across 30 papers - about 2 per paper it appears in.

4.What is the difficulty level of Definite Integration questions in JEE Advanced?

Of the 52 questions analysed for this chapter, 21% are easy, 46% moderate and 33% tough. 2015 had the most, with 7 questions.

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

These topics have carried the most weightage in Definite Integration:

  • Properties of Definite Integration - 22 questions (42%)
  • Leibnitz Rule of Differentiation - 7 questions (13%)
  • Definite Integration by Parts - 6 questions (12%)
  • Properties of Definite Integration has produced the most tough questions (7).
6.Is Definite Integration's weightage in JEE Advanced going up or down?

Across all 30 papers analysed, Definite Integration has averaged about 1.7 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.