JEE Main 2020MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2020 — Indefinite Integration Question with Solution

JEE Main 2020 (04 Sep Shift 1)

Question

Let fx=∫x1+x2dx  x≥0. Then f3-f1 is equal to :

Choose an option

Show full solutionCorrect option: D
Correct answer
Dπ12+12-34

Step-by-step explanation

fx=∫x1+x2dx

Let x=tan2θ

dx=2tanθsec2θ dθ

fx=∫tanθ1+tan2θ2.2tanθsec2θ dθ

fx=∫tanθsec4θ.2tanθsec2θ dθ

fx=∫2tan2θ.cos2θ dθ

fx=∫2sin2θ dθ

fx=∫1−cos2θ dθ

fx=θ−sin2θ2+C=θ−tanθ1+tan2θ+C

fx=tan−1x−x1+x+C

Now, f3−f1=tan−3−31+3−tan−11+11+1

=π3−π4+12−34=π12+12-34

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About this question

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