JEE Main 2022MathematicsDefinite IntegrationMediumMCQ

JEE Main 2022 — Definite Integration Question with Solution

JEE Main 2022 (29 Jun Shift 1)

Question

∫05cosπx-x2dx, where t denotes greatest integer less than or equal to t, is equal to

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Show full solutionCorrect option: A
Correct answer
A0

Step-by-step explanation

I=∫05cosx2π-πxdx

∵x∈0,5 ∴x∈0,52⇒x2∈0,1,2

I=∫02cos-πxdx+∫24cosπ-πxdx+∫45cos2π-πxdx

⇒I=sinπxπ02+-sinπxπ24+sinπxπ45=0

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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.