JEE Main 2021MathematicsArea Under CurvesMediumMCQ

JEE Main 2021 — Area Under Curves Question with Solution

JEE Main 2021 (01 Sep Shift 2)

Question

The area, enclosed by the curves y=sinx+cosx and y=|cosx-sinx| and the lines x=0, x=π2, is :

Choose an option

Show full solutionCorrect option: B
Correct answer
B22(2-1)

Step-by-step explanation

A=∫0π/2((cosx+sinx)-|cosx-sinx|)dx

A=∫0π/4((cosx+sinx)-(cosx-sinx))dx+∫π/4π/2((cosx+sinx)-(sinx-cosx))dx

A=2∫0π/4sinxdx+2∫π/4π/2cosxdx

=2-12+1+21-12=4-22=22(2-1)

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About this question

This is a previous-year question from JEE Main 2021, covering the Area Under Curves 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.