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Mathematics - Indefinite Integration

Practise 77 NDA previous year questions on Indefinite Integration, compiled from papers spanning 2010 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 NDA tests.

Indefinite Integration has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 77 questions in all. 19% of them were easy, 77% moderate and 4% tough. Most of its questions came from 2010, with 8 questions that year. In the last three years (2024–2026) it had 12 questions across 5 papers, about 2.4 per paper.

The chapter's 3 topics are not weighted equally: Integration by Substitution (57 questions, 74%), Integration by Parts (15 questions, 19%), and Fundamental of Indefinite Integration (5 questions, 6%) have been asked the most. Integration by Substitution has also led over the last five years, with 16 questions. Integration by Substitution has produced the most tough questions (3).

  1. 1Passage: Let . Question: What is the value of ?2026 (Phase 1)Integration by Substitution
  2. 2Passage: Let . Question: What is the value of ?2026 (Phase 1)Integration by Substitution
  3. 3Consider the following for the two (02) items that follow: Let the function , where and is an integer. What is equal to?2025 (Phase 1)Integration by Substitution
  4. 4For the following two (02) items: Let and . What is equal to?2025 (Phase 2)Integration by Parts
  5. 5For the following two (02) items: Let and . Consider the following: I. II. Which of the above is/are correct?2025 (Phase 2)Integration by Parts
  6. 6What is equal to?2025 (Phase 2)Integration by Substitution
  7. 7Given that What is the value of ?2024 (Phase 1)Integration by Substitution
  8. 8Given that What is the value of ?2024 (Phase 1)Integration by Substitution
  9. 9Let What is the value of ?2024 (Phase 1)Integration by Substitution
  10. 10Let What is the value of ?2024 (Phase 1)Integration by Substitution
  11. 11Paragraph: Let Question: What is equal to?2024 (Phase 2)Integration by Substitution
  12. 12Paragraph: Let Question: What is equal to?2024 (Phase 2)Integration by Substitution
  13. 13Paragraph: Let , where are real numbers. Further and Question: What is the value of Q ?2023 (Phase 1)Integration by Substitution
  14. 14Paragraph: Let , where are real numbers. Further and Question: What is the value of R ?2023 (Phase 1)Integration by Substitution
  15. 15What is equal to?2022 (Phase 1)Integration by Substitution
  16. 16If and , then what is equal to?2022 (Phase 1)Integration by Substitution
  17. 17What is equal to?2022 (Phase 2)Integration by Substitution
  18. 18What is equal to?2022 (Phase 2)Integration by Parts
  19. 19What is equal to?2022 (Phase 2)Integration by Substitution
  20. 20What is equal to ?2021 (Phase 1)Integration by Substitution
  21. 21What is equal to ?2021 (Phase 1)Integration by Substitution
  22. 22What is equal to?2021 (Phase 1)Integration by Substitution
  23. 23What is equal to?2021 (Phase 2)Integration by Substitution
  24. 24What is the integral of with respect to2021 (Phase 2)Integration by Substitution
  25. 25If , where , then which one of the following is correct?2021 (Phase 2)Integration by Substitution
  26. 26If , then what is equal to?2020Integration by Substitution
  27. 27What is equal to ?2020Integration by Parts
  28. 28What is equal to?2020Integration by Substitution
  29. 29What is the value of such that integration of with respect to , may be a rational function?2020Integration by Substitution
  30. 30What is equal to ?2019 (Phase 1)Integration by Parts
  31. 31What is equal to ?2019 (Phase 1)Integration by Substitution
  32. 32What is equal to?2019 (Phase 2)Integration by Substitution
  33. 33What is equal to ?2019 (Phase 2)Integration by Substitution
  34. 34What is equal to?2018 (Phase 1)Integration by Substitution
  35. 35What is equal to? Where c is the constant o integration.2018 (Phase 2)Integration by Substitution
  36. 36What is equal to? Where c is the constant of integration.2018 (Phase 2)Integration by Substitution
  37. 37What is equal to?2018 (Phase 2)Integration by Substitution
  38. 38What is equal to?2017 (Phase 1)Integration by Substitution
  39. 39What is equal to?2017 (Phase 1)Integration by Substitution
  40. 40Let be an indefinite integral of . Consider the following statements : Statement 1 : The function satisfies for all real x . Statement for a2017 (Phase 1)Fundamental of Indefinite Integration
  41. 41What is equal to?2017 (Phase 2)Integration by Substitution
  42. 42is equal to2017 (Phase 2)Integration by Parts
  43. 43Consider the function . Let and be twice differentiable functions on satisfying and . Then what is at equal to ?2016 (Phase 1)Integration by Substitution
  44. 44What is equal to?2016 (Phase 2)Integration by Substitution
  45. 45What is equal to?2016 (Phase 2)Integration by Parts
  46. 46What is equal to? where is the constant integration.2015 (Phase 1)Integration by Parts
  47. 47The integral is of the form . What is equal to?2015 (Phase 1)Integration by Substitution
  48. 48The integral is of the form . What is equal to?2015 (Phase 1)Integration by Substitution
  49. 49What is equal to? where is the constant of integration.2015 (Phase 1)Integration by Substitution
  50. 50is equal to where is the constant of integration2015 (Phase 2)Integration by Substitution

Frequently Asked Questions

1.How many questions are available for Indefinite Integration?

This chapter includes 77 questions compiled from NDA papers spanning 2010 to 2026.

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

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

3.Is Indefinite Integration an important chapter for NDA Mathematics?

Indefinite Integration has appeared in 17 of the 17 years of NDA papers covered here, with 77 questions across 30 papers - about 3 per paper it appears in.

4.What is the difficulty level of Indefinite Integration questions in NDA?

Of the 77 questions analysed for this chapter, 19% are easy, 77% moderate and 4% tough. 2010 had the most, with 8 questions.

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

These topics have carried the most weightage in Indefinite Integration:

  • Integration by Substitution - 57 questions (74%)
  • Integration by Parts - 15 questions (19%)
  • Fundamental of Indefinite Integration - 5 questions (6%)
  • Integration by Substitution has produced the most tough questions (3).
6.Is Indefinite Integration's weightage in NDA going up or down?

Across all 30 papers analysed, Indefinite Integration has averaged about 2.6 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 2.4 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.