JEE Main 2021MathematicsArea Under CurvesMediumMCQ

JEE Main 2021 — Area Under Curves Question with Solution

JEE Main 2021 (26 Feb Shift 2)

Question

Let A1 be the area of the region bounded by the curves y=sinx,y=cosx and y-axis in the first quadrant. Also, let A2 be the area of the region bounded by the curves y=sinx,y=cosx, x-axis and x=π2 in the first quadrant. Then,

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Show full solutionCorrect option: B
Correct answer
BA1:A2=1:2 and A1+A2=1

Step-by-step explanation

A1=∫0π/4cosx-sinxdx

A1=sinx+cosx0π/4=2-1

A2=∫0π/4sinxdx+∫π/4π/2cosxdx

=-cosx0π/4+sinxπ/4π/2

A2=1-12+1-12=2-2

A1:A2=1:2, A1+A2=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.