JEE Main 2023MathematicsIndefinite IntegrationHardMCQ

JEE Main 2023 — Indefinite Integration Question with Solution

JEE Main 2023 (10 Apr Shift 1)

Question

If Ix=∫esin2xcosx sin2x-sinxdx and I0=1, then Iπ3 is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B12e34

Step-by-step explanation

Given,

Ix=∫esin2xcosx sin2x-sinxdx

⇒Ix=∫esin2xcosx-12 cosxsin2x dx

Now let, sin2x=t⇒sin2x dx=dt

Ix=∫et1-t-121-tdt

Now comparing with,

Ix=∫etft+f'tdt=etft+c

Here, ft=1-t & f't=-121-t

⇒Ix=et1-t+c=esin2x·cosx+c

Now using, I0=1⇒c=0

Hence, the value of Iπ3=12e34

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About this question

This is a previous-year question from JEE Main 2023, 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.