JEE Main 2019MathematicsDefinite IntegrationEasyMCQ

JEE Main 2019 — Definite Integration Question with Solution

JEE Main 2019 (12 Apr Shift 1)

Question

If ∫0π2cotxcotx+cosecxdx=m(π+n), then mn is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C-1

Step-by-step explanation

Let I=∫0π2cotxcotx+cosecxdx
⇒I=∫0π2cosxcosx+1dx
⇒I=∫0π2cosx+1-1cosx+1dx
⇒I=∫0π21-12cos2x2dx
⇒I=∫0π21-12sec2x2dx
⇒I=x-tanx20π2
⇒I=π2-1-0-0
⇒I=π2-1=12π-2.

Now using given information ∫0π2cotxcotx+cosecxdx=m(π+n), clearly m=12 and n=-2.

⇒mn=-1

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Definite Integration chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2019, 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.