JEE Main 2020MathematicsDefinite IntegrationMediumMCQ

JEE Main 2020 — Definite Integration Question with Solution

JEE Main 2020 (03 Sep Shift 2)

Question

If the value of the integral ∫012x21-x232dx is k6, then k is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B23-π

Step-by-step explanation

k6=∫012x21-x232dx

Let x=sinθ⇒dx=cosθdθ

⇒k6=∫0π6sin2 θ1-sin2 θ32cosθdθ⇒k6=∫0π6sin2 θcos3 θcosθdθ

⇒k6=∫0π6tan2θdθ=∫0π6sec2θ-1dθ⇒k6=tanθ-θ0π6=13-π6=23-π6

⇒k=23-π

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About this question

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