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Mathematics - Definite Integration

Practise 314 JEE Main previous year questions on Definite Integration, compiled from papers spanning 2002 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 Main tests.

Definite Integration has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 314 questions in all. 11% of them were easy, 44% moderate and 45% tough. Most of its questions came from 2021, with 51 questions that year. In the last three years (2024–2026) it had 71 questions across 49 papers, about 1.4 per paper.

The chapter's 11 topics are not weighted equally: Properties of Definite Integration (143 questions, 46%), Leibnitz Rule of Differentiation (46 questions, 15%), and Definite Integration by Substitution (42 questions, 13%) have been asked the most. Properties of Definite Integration has also led over the last five years, with 70 questions. Properties of Definite Integration has produced the most tough questions (49).

  1. 1The value of the integral is equal to:08 Apr, 2026 (E)Definite Integration by Substitution
  2. 2If , then is equal to ________.08 Apr, 2026 (E)Definite Integration by Substitution
  3. 3The value of the integral is:06 Apr, 2026 (M)Properties of Definite Integration
  4. 4Let be a singular matrix. Let , . If and are respectively the maximum and the minimum values of in , then is equal to :06 Apr, 2026 (E)Properties of Definite Integration
  5. 5Let be such that , for all and . Let be a differentiable function such that . Then is equal to :06 Apr, 2026 (E)Leibnitz Rule of Differentiation
  6. 6The value of the integral is equal to :06 Apr, 2026 (E)Properties of Definite Integration
  7. 7The value of the integral is:05 Apr, 2026 (M)Definite Integration by Substitution
  8. 8The value of the integral is:05 Apr, 2026 (M)Definite Integration by Substitution
  9. 9Let , , be in A.P. and be the minimum value of . Then the value of the integral is :05 Apr, 2026 (E)Definite Integration by Substitution
  10. 10Let be a differentiable function defined as . Then the value of is :05 Apr, 2026 (E)Leibnitz Rule of Differentiation
  11. 11Let , where is the greatest integer function. Then equals:04 Apr, 2026 (M)Properties of Definite Integration
  12. 12The integral is equal to:04 Apr, 2026 (E)Definite Integration by Parts
  13. 13Let be a twice differentiable function such that , . Then is equal to ______04 Apr, 2026 (E)Leibnitz Rule of Differentiation
  14. 14Let denote the greatest integer function. Then the value of is :02 Apr, 2026 (M)Properties of Definite Integration
  15. 15If , then is equal to _______.02 Apr, 2026 (M)Miscellaneous
  16. 16The value of is equal to:02 Apr, 2026 (E)Properties of Periodic Functions
  17. 17Let be a polynomial function such that , for all . Then is equal to28 Jan, 2026 (M)Properties of Definite Integration
  18. 18If , where C is the constant of integration, then is equal to28 Jan, 2026 (M)Definite Integration by Parts
  19. 19The value of is28 Jan, 2026 (M)Properties of Definite Integration
  20. 20Let denote the greatest integer function. Then is equal to :28 Jan, 2026 (E)Properties of Definite Integration
  21. 21Let a differentiable function satisfy the equation . If is a standard parabola passing through the points and , then is equal to .24 Jan, 2026 (M)Leibnitz Rule of Differentiation
  22. 22If satisfies the relation , then is equal to .24 Jan, 2026 (E)Leibnitz Rule of Differentiation
  23. 23The value of the integral is :23 Jan, 2026 (M)Properties of Definite Integration
  24. 24The number of elements in the set and is .23 Jan, 2026 (E)Leibnitz Rule of Differentiation
  25. 25The value of , where denotes the greatest integer function, is22 Jan, 2026 (M)Properties of Definite Integration
  26. 26Let , where [] is the greatest integer funtion. Then22 Jan, 2026 (E)Properties of Definite Integration
  27. 27Let be the greatest integer function. If , then is equal to .22 Jan, 2026 (E)Properties of Definite Integration
  28. 28The value of is equal to:21 Jan, 2026 (M)Properties of Definite Integration
  29. 29is equal to .21 Jan, 2026 (M)Properties of Definite Integration
  30. 30If , where , then is equal to .21 Jan, 2026 (E)Definite Integration by Substitution
  31. 31Let be a positive function and and . Then the value of is equal to ________08 Apr, 2025 (E)Properties of Definite Integration
  32. 32The integral is equal to:08 Apr, 2025 (E)Properties of Definite Integration
  33. 33The integral is equal to :07 Apr, 2025 (M)Properties of Definite Integration
  34. 34The value of is equal to04 Apr, 2025 (M)Properties of Definite Integration
  35. 35Let the domain of the function be . If where [ is the greatest integer function, then is equal to03 Apr, 2025 (M)Properties of Definite Integration
  36. 36The integral is equal to03 Apr, 2025 (E)Properties of Definite Integration
  37. 37Let [.] denote the greatest integer function. If , then is equal to _______ .02 Apr, 2025 (M)Properties of Definite Integration
  38. 38Let be the point of intersection of the curve and the straight line in the second quadrant. Then the integral is equal to :02 Apr, 2025 (E)Properties of Definite Integration
  39. 39is equal to :02 Apr, 2025 (E)Properties of Definite Integration
  40. 40The integral \(80 _0^{ { }{4}} ( { + }{9+16 2 } ) d \) is equal to :29 Jan, 2025 (M)Definite Integration by Substitution
  41. 41Let \(f:(0, ) {R}\) be a twice differentiable function. If for some \( {a} 0, _0^1 f( x) {d} = {a} f(x), f(1)=1\) and \(f(16)= {1}{8}\), the29 Jan, 2025 (M)Leibnitz Rule of Differentiation
  42. 42Let . If the range of is , then equals :29 Jan, 2025 (E)Leibnitz Rule of Differentiation
  43. 43If , where denotes the greatest integer function, then is equal to _______.29 Jan, 2025 (E)Properties of Definite Integration
  44. 44Let for some function and . Then is equal to28 Jan, 2025 (M)Leibnitz Rule of Differentiation
  45. 45If , then equals28 Jan, 2025 (M)Properties of Definite Integration
  46. 46Let be a real valued continuous function defined on the positive real axis such that . If , then value of is :28 Jan, 2025 (E)Leibnitz Rule of Differentiation
  47. 47Let be a twice differentiable function such that . If for all , and , then is equal to :28 Jan, 2025 (E)Definite Integration by Parts
  48. 48, then is24 Jan, 2025 (M)Walli's Formula
  49. 49The value of is23 Jan, 2025 (M)Properties of Definite Integration
  50. 50If , then equals :23 Jan, 2025 (E)Properties of Definite Integration

Frequently Asked Questions

1.How many questions are available for Definite Integration?

This chapter includes 314 questions compiled from JEE Main papers spanning 2002 to 2026.

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

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

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

Definite Integration has appeared in 25 of the 25 years of JEE Main papers covered here, with 314 questions across 191 papers - about 2 per paper it appears in.

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

Of the 314 questions analysed for this chapter, 11% are easy, 44% moderate and 45% tough. 2021 had the most, with 51 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 - 143 questions (46%)
  • Leibnitz Rule of Differentiation - 46 questions (15%)
  • Definite Integration by Substitution - 42 questions (13%)
  • Properties of Definite Integration has produced the most tough questions (49).
6.Is Definite Integration's weightage in JEE Main going up or down?

Across all 191 papers analysed, Definite Integration has averaged about 1.6 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.4 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.