JEE Main 2021MathematicsDefinite IntegrationMediumNumerical

JEE Main 2021 — Definite Integration Question with Solution

JEE Main 2021 (24 Feb Shift 1)

Question

If ∫-aax+x-2dx=22, a>2 and x denotes the greatest integer ≤x, then ∫a-ax+xdx is equal to

Enter your answer

Show full solutionCorrect answer: 3
Correct answer
3

Step-by-step explanation

∫-a0-2x+2dx+∫02x+2-xdx+∫2a2x-2dx=22

⇒-x2+2x|-a0+2x|02+x2-2x|0a=22

⇒a2+2a+4+a2-2a=22

⇒2a2=18⇒a=3 (a≠-3)

∫3-3x+xdx=∫3-3xdx+∫3-3xdx=0+--3-2-1+1+2=3

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 2021, 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.