JEE Main 2023MathematicsDefinite IntegrationHardMCQ

JEE Main 2023 — Definite Integration Question with Solution

JEE Main 2023 (01 Feb Shift 2)

Question

The value of the integral ∫-π4π4x+π42-cos2xdx is :

Choose an option

Show full solutionCorrect option: D
Correct answer
Dπ263

Step-by-step explanation

Let,

I=∫-π4π4x+π42-cos2xdx         …1

Now replacing x→-x we get,

⇒I=∫-π4π4-x+π42-cos2xdx          …2

Now both the equation we get,

⇒2I=∫-π4π4π22-cos2xdx

⇒I=π4·2∫0π4dx2-cos2xdx as cos2x is even function

⇒I=π4·2∫0π41+tan2xdx21+tan2x-1-tan2x

⇒I=π4·2∫0π4sec2xdx3tan2x+1

Now let tanx=t⇒sec2xdx=dt

⇒I=π2∫01dt3t2+1

⇒I=π23tan-13

⇒I=π263

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About this question

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