JEE Main 2021MathematicsDefinite IntegrationMediumMCQ

JEE Main 2021 — Definite Integration Question with Solution

JEE Main 2021 (27 Aug Shift 2)

Question

The value of the integral ∫01xdx(1+x)(1+3x)(3+x) is:

Choose an option

Show full solutionCorrect option: C
Correct answer
Cπ81−32

Step-by-step explanation

Let x=t

⇒x=t2, dx=2tdt

Let I=∫01xdx(1+x)(1+3x)(3+x)

I=∫01 2t2dtt2+13t2+1t2+3

=∫01 3t2+1−t2+1dtt2+13t2+1t2+3

=∫01 1t2+3t2+1−1t2+33t2+1dt

=∫01 dt2t2+1−183dt3t2+1−38dtt2+3

=12tan−1⁡t−338×3tan−1⁡3t−383tan−1⁡t301

=π8−38×π3−38×π6

=π8−3π16

=π81−32

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About this question

This is a previous-year question from JEE Main 2021, 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.