JEE Main 2022MathematicsArea Under CurvesEasyNumerical

JEE Main 2022 — Area Under Curves Question with Solution

JEE Main 2022 (24 Jun Shift 2)

Question

The area (in sq. units) of the region enclosed between the parabola y2=2x and the line x+y=4 is ______.

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Show full solutionCorrect answer: 18
Correct answer
18

Step-by-step explanation

y2=2x ⇒y2=24-y

⇒y2+2y-8=0  ⇒y=-4,2

The point of intersection of y2=2x and x+y=4 are 8,-4 and 2,2

Area =∫-424-y-y22dy =4y-y22-y36-42

=8-2-43--16-8+323

=543=18 Sq.units.

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About this question

This is a previous-year question from JEE Main 2022, 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.