JEE Main 2020MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2020 — Indefinite Integration Question with Solution

JEE Main 2020 (08 Jan Shift 1)

Question

If ∫cosxdxsin3x1+sin6x23=fx1+sin6x1λ+c, where c is a constant of integration, then λfπ3 is equal to

Choose an option

Show full solutionCorrect option: D
Correct answer
D-2

Step-by-step explanation

Let, sinx=t 

cosxdx=dt
I=∫dtt31+t623=∫dtt71+1t623

Put 1+1t6=r3 

⇒dtt7=-12r2dr

I=-12∫r2drr2=-12r+c 

⇒I=-12sin6x+1sin6x13+c

⇒I=-12sin2x1+sin6x13+c

So, fx=-12cosec2x and λ=3

λfπ3=-2

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About this question

This is a previous-year question from JEE Main 2020, 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.