JEE Main 2017MathematicsDefinite IntegrationMediumMCQ

JEE Main 2017 — Definite Integration Question with Solution

JEE Main 2017 (09 Apr Online)

Question

If ∫12dxx2-2x+432=kk+5, then k is equal to

Choose an option

Show full solutionCorrect option: D
Correct answer
D1

Step-by-step explanation

∫ 1 2 dx ( ( x−1 ) 2 +3 ) 3 2

Substituting x-1=3tan⁡θ​

⇒dx=3sec2θ·dθ​

Now ∫0π63 sec 2 θ​ ⁡dθ​33 sec 3 θ​

=13∫0π6cosθdθ​=13sin⁡θ0π6=16

⇒16=kk+5=k+5=6k

=k=1.

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About this question

This is a previous-year question from JEE Main 2017, 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.