JEE Main 2024MathematicsDefinite IntegrationHardNumerical

JEE Main 2024 — Definite Integration Question with Solution

JEE Main 2024 (31 Jan Shift 1)

Question

If the integral 525∫0π2sin2x cos112x1+cos52x12dx is equal to n2−64, then n is equal to ________

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Show full solutionCorrect answer: 176
Correct answer
176

Step-by-step explanation

Let,

I=∫0π2sin2x cos112x1+cos52x12dx

Let cosx=t2⇒sinxdx=-2t dt

∴I=-4∫10t2⋅t111+t5tdt

⇒I=4∫01t141+t5dt

Now, let 1+t5=k2

⇒5t4dt=2k dk

∴I=4⋅∫12k2−12⋅k·2k5dk

⇒I=85∫12k6−2k4+k2 dk

⇒I=85k77−2k55+k3312

⇒I=85827−825+223−17+25−13

⇒I=85222105−8105

⇒525⋅I=1762−64

Hence, on comparing we get, n=176

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About this question

This is a previous-year question from JEE Main 2024, covering the Definite 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.