JEE Main 2022MathematicsDefinite IntegrationMediumMCQ

JEE Main 2022 — Definite Integration Question with Solution

JEE Main 2022 (26 Jul Shift 1)

Question

If a=limn→∞∑k=1n2nn2+k2 and fx=1-cosx1+cosx,x∈0,1, then:

Choose an option

Show full solutionCorrect option: C
Correct answer
C2fa2=f'a2

Step-by-step explanation

Given, a=limn→∞∑k=1n2nn2+k2

⇒a=1n∑k=1n21+kn2=∫0121+x2dx

⇒a=2tan-1x01

⇒a=2π4-0=π2

Now, fx=1-cosx1+cosx

⇒fx=tanx2;x∈0,1

So, fa2=fπ4

⇒fπ4=2-1

And f'π4=12sec2π8=22+1

So, f'π4=2fπ4

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 2022, 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.