JEE Main 2017MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2017 — Indefinite Integration Question with Solution

JEE Main 2017 (08 Apr Online)

Question

The integral ∫1+2cotxcosecx+cotxdx, 0<x<π2 is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A2logsinx2+c

Step-by-step explanation

Let I=∫1+2cotxcosec x+cotxdx  

⇒I=∫2cotxcosecx+cosec2x+cot2xdx

⇒I=∫cosec x+cot x2dx

⇒I=∫cosec x+cot xdx

⇒I=∫cosec x+cotxdx

⇒I=logtanx2+logsinx+c, where c is the constant of integration.
⇒I=logsinx2cosx2·2sinx2cosx2+c
⇒I=2logsinx2+c

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About this question

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