JEE Main 2021MathematicsArea Under CurvesHardMCQ

JEE Main 2021 — Area Under Curves Question with Solution

JEE Main 2021 (18 Mar Shift 2)

Question

The area (in sq. unit) bounded by the curve 4y2=x2(4-x)(x-2) is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C3π2

Step-by-step explanation

4y2=x2(4-x)(x-2)

y=|x|2(4-x)(x-2)

⇒y1=x2(4-x)(x-2)

and y2=-x2(4-x)(x-2)

D:x∈[2,4]

Required Area

=∫24y1-y2dx=∫24x(4-x)(x-2)dx   ...1

Applying ∫abfxdx=∫abfa+b-xdx

Area =∫246-x(4-x)(x-2)dx   ...2

(1)+(2)

2A=6∫24(4-x)(x-2)dx

A=3∫241-(x-3)2dx

A=3·π2·12=3π2 sq. unit

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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.