JEE Main 2023MathematicsArea Under CurvesHardMCQ

JEE Main 2023 — Area Under Curves Question with Solution

JEE Main 2023 (13 Apr Shift 1)

Question

The area of the region enclosed by the curve fx=max{sinx,cosx},-π≤x≤π and the x-axis is

Choose an option

Show full solutionCorrect option: B
Correct answer
B4

Step-by-step explanation

Plotting the required diagram we get,

Now from diagram we can say that,

sinx is maximum for x∈-π,-3π4∪π4,π and cosx is maximum for x∈-3π4,-π2∪-π2,π4

So, area of the region is given by,

A=∫-π-3π4sinxdx+∫π4πsinxdx+∫-3π4-π2cosxdx+∫-π2π4cosxdx

⇒A=12-1+1+12+-1+12+12+1

⇒A=2+22+2-22=4

Hence this is the required option.

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About this question

This is a previous-year question from JEE Main 2023, 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.