JEE Main 2021MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2021 — Indefinite Integration Question with Solution

JEE Main 2021 (24 Feb Shift 1)

Question

If ∫cosx-sinx8-sin2x dx=asin-1sinx+cosx b+c, where c is a constant of integration, then the ordered pair a,b is equal to:

Choose an option

Show full solutionCorrect option: D
Correct answer
D1,3

Step-by-step explanation

∫cosx-sinx8-sin2xdx

=∫cosx-sinx9-sinx+cosx2dx

Let sinx+cosx=t

∫dt9-t2=sin-1t3+c

=sin-1sinx+cosx3+c

So a=1, b=3

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About this question

This is a previous-year question from JEE Main 2021, covering the Indefinite Integration chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.