JEE Main 2023MathematicsArea Under CurvesMediumNumerical

JEE Main 2023 — Area Under Curves Question with Solution

JEE Main 2023 (30 Jan Shift 1)

Question

Let α be the area of the larger region bounded by the curve y2=8x and the lines y=x and x=2, which lies in the first quadrant. Then the value of 3α is equal to

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Show full solutionCorrect answer: 22
Correct answer
22

Step-by-step explanation

We have,

y2=8x

y=x

Point of intersection of curve and a line is A8,8.

Required area

α=∫288x-xdx

⇒α=42x323-x2228

⇒α=422233-642-42233-42

⇒α=1123-30

⇒α=223

So, 3α=22

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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.