JEE Main 2024MathematicsArea Under CurvesHardMCQ

JEE Main 2024 — Area Under Curves Question with Solution

JEE Main 2024 (31 Jan Shift 1)

Question

The area of the region x, y:y2≤4x, x<4, xyx-1x-2x-3x-4>0, x≠3 is

Choose an option

Show full solutionCorrect option: D
Correct answer
D323

Step-by-step explanation

Given: y2≤4x, x<4, xyx-1x-2x-3x-4>0

Case - I: y>0

⇒xx-1x-2x-3x-4>0

⇒x∈0, 1∪2, 3   ...i

Case – II : y<0

xx-1x-2x-3x-4<0

⇒x∈1, 2∪3, 4   ...ii

So, the required area is given by,

A=∫044xdx {Take the mirror image of strips in the first quadrant to find the area}

⇒A=2∫04xdx

⇒A=2·23x3204

⇒A=2·23432

⇒A=2×23×8

⇒A=323

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About this question

This is a previous-year question from JEE Main 2024, 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.