JEE Main 2014MathematicsDefinite IntegrationMediumMCQ

JEE Main 2014 — Definite Integration Question with Solution

JEE Main 2014 (09 Apr Online)

Question

The integral ∫012ln1+2x1+4x2dx equals

Choose an option

Show full solutionCorrect option: B
Correct answer
Bπ16ln2

Step-by-step explanation

We have, I=∫012ln1+2x1+4x2dx

Let, 2x=tanθ⇒dx=12sec2θdθ

⇒I=∫0π4ln1+tanθsec2θ·12·sec2θdθ  ∵ 1+tan2θ=sec2θ
 =12∫0π4ln1+tanθdθ
  =12∫0π4ln1+tanπ4-θdθ 

∵∫0afxdx=∫0afa-xdx=12∫0π4ln1+1-tanθ1+tanθdθ

 =12∫0π4ln21+tanθdθ=12ln2∫0π4dθ-∫0π4ln1+tanθdθ
⇒2I=ln2π4-2I

⇒I=π16ln2

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About this question

This is a previous-year question from JEE Main 2014, 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.