JEE Main 2016MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2016 — Indefinite Integration Question with Solution

JEE Main 2016 (09 Apr Online)

Question

If ∫dxcos3x 2sin2x=tanxA+CtanxB+k, where k is a constant of integration, then A+B+C equals 

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Show full solutionCorrect option: A
Correct answer
A165

Step-by-step explanation

∫dxcos3x4sinxcosx=∫dx2cos4xtanx

Let, tanx=t2⇒sec2x=1+t4

And sec2xdx=2tdt

∴I= ∫sec4xdx2tanx= ∫sec2x.sec2xdx2tanx

=∫1+t42t dt2t=∫1+t4dt

=t+t55+k, where k is a constant of integration.

= tanx+15tan52x+k 

Where, t= tanx.

A=12, B=52, C=15

A+B+C=165

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About this question

This is a previous-year question from JEE Main 2016, 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.