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Mathematics - Indefinite Integration

Practise 58 KCET previous year questions on Indefinite Integration, compiled from papers spanning 2007 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 KCET tests.

Indefinite Integration has been asked in 20 of the 20 years of KCET papers analysed (2007–2026), with 58 questions in all. 36% of them were easy, 38% moderate and 26% tough. Most of its questions came from 2020, with 5 questions that year. In the last three years (2024–2026) it had 7 questions across 3 papers, about 2.3 per paper.

The chapter's 6 topics are not weighted equally: Integration by Substitution (27 questions, 47%), Integration using Partial Fraction (10 questions, 17%), and Integration by Parts (10 questions, 17%) have been asked the most. Integration by Substitution has also led over the last five years, with 7 questions. Integration by Substitution has produced the most tough questions (7).

  1. 1If ' ' is a natural number, then2026Integration by Substitution
  2. 2Preview not available - open to view this question.2026Fundamental of Indefinite Integration
  3. 3The value of is2025Integration using Partial Fraction
  4. 4equals2025Integration by Substitution
  5. 5Preview not available - open to view this question.2024Integration by Substitution
  6. 6is2024Integration using Partial Fraction
  7. 7is2024Integration by Substitution
  8. 8is equals to2023Integration by Substitution
  9. 9is equals to2023Miscellaneous Forms
  10. 10is equals to2023Integration by Substitution
  11. 11is equal to2022Integration by Substitution
  12. 12If , then2022Integration using Partial Fraction
  13. 13is equal to2021Integration by Substitution
  14. 14The value of is equal to2021Integration by Substitution
  15. 15The value of is equal to2021Fundamental of Indefinite Integration
  16. 16The value of is equal to2021Integration by Substitution
  17. 17If the curves and intersect perpendicularly, then the value of is2020Integration by Substitution
  18. 18If the side of a cube is increased by , then the surface area of a cube is increased by2020Integration by Substitution
  19. 19The value of is2020Integration by Parts
  20. 20The maximum value of , if is2020Integration using Partial Fraction
  21. 21The value of is2020Integration by Substitution
  22. 22\( {1}{ {x}+x {x}} d x= \)2019Integration by Substitution
  23. 23\( {2 x-1}{(x-1)(x+2)(x-3)} d x=A |x-1|+B |x+2|+C |x-3|+K \), then \( A, B \), C are respectively2019Integration using Partial Fraction
  24. 24\( x^{3} 3 x d x= \)2019Integration by Parts
  25. 25\( {1}{1+e^{x}} d x \) is equal to2018Fundamental of Indefinite Integration
  26. 26\( {1}{ {3-6 x-9 x^{2}}} d x \) is equal to2018Fundamental of Indefinite Integration
  27. 27\( e^{ x} ( { x+1}{ x} ) d x \) is equal to2018Integration by Parts
  28. 28The range of the function \( f(x)= {9-x^{2}} \) is2017Integration by Substitution
  29. 29If \( ^{-1} x+ ^{-1} y= {4 }{5} \), then \( ^{-1} x+ ^{-1} y \) is equal to2017Integration using Partial Fraction
  30. 30Let \( = | {array}{ccc}A x & x^{2} & 1 \\ B y & y^{2} & 1 \\ C z & z^{2} & 1 {array} | \) and \( _{1}= | {array}{cccc}A & B & C & \\ x & y &2017Integration by Substitution
  31. 31The value of \( {e^{x}(1+x) d x}{ ^{2} (e^{x} x )} \) is equal to2016Integration by Substitution
  32. 32The value of \( {e^{x} (x^{2} ^{-1} x+ ^{-1} x+1 )}{x^{2}+1} d x \) is equal to2016Integration by Substitution
  33. 33The value of \( {e^{6 x}-e^{5 x}}{e^{4 x}-e^{3 x}} {dx} \) is equal to2016Miscellaneous Forms
  34. 34The probability distribution of \( x \) is find the value of \( k \)2015Integration by Substitution
  35. 35If \( 2 ^{-1} x+ ^{-1} x \), then2015Miscellaneous Forms
  36. 36If \( A= [ {array}{cc}0 & 1 \\ 1 & 0 {array} ] \), then \( A^{2} \) equal to2015Integration by Parts
  37. 37The symmetric part of the matrix \( A= ( {array}{ccc}1 & 2 & 4 \\ 6 & 8 & 2 \\ 2 & -2 & 7 {array} ) \) is2014Integration by Parts
  38. 38Consider the following statements : (a) If any two rows or columns of a determinant are identical, then the value of the determinant is zero2014Integration by Substitution
  39. 39where, is equal to2013Integration by Substitution
  40. 40is equal to2013Integration by Parts
  41. 41If , then is equal to2013Integration using Partial Fraction
  42. 42If , then is equal to2012Integration using Partial Fraction
  43. 43If and , then is equal to2012Integration using Reduction Formula
  44. 44is2011Integration by Parts
  45. 45When , then is2011Integration by Substitution
  46. 46If , then A : is2010Integration using Partial Fraction
  47. 47If where is the constant of integration, then is2010Integration by Substitution
  48. 48If , then is2010Integration by Substitution
  49. 49is equal to2009Integration by Parts
  50. 50is equal to2009Miscellaneous Forms

Frequently Asked Questions

1.How many questions are available for Indefinite Integration?

This chapter includes 58 questions compiled from KCET papers spanning 2007 to 2026.

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

These are KCET 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 KCET Mathematics?

Indefinite Integration has appeared in 20 of the 20 years of KCET papers covered here, with 58 questions across 20 papers - about 3 per paper it appears in.

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

Of the 58 questions analysed for this chapter, 36% are easy, 38% moderate and 26% tough. 2020 had the most, with 5 questions.

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

These topics have carried the most weightage in Indefinite Integration:

  • Integration by Substitution - 27 questions (47%)
  • Integration using Partial Fraction - 10 questions (17%)
  • Integration by Parts - 10 questions (17%)
  • Integration by Substitution has produced the most tough questions (7).
6.Is Indefinite Integration's weightage in KCET going up or down?

Across all 20 papers analysed, Indefinite Integration has averaged about 2.9 questions per paper. In the last three years (2024–2026), that average has fallen, at about 2.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.