JEE Main 2022MathematicsArea Under CurvesHardNumerical

JEE Main 2022 — Area Under Curves Question with Solution

JEE Main 2022 (24 Jun Shift 1)

Question

Let S be the region bounded by the curves y=x3 and y2=x. The curve y=2x divides S into two regions of areas R1 and R2. If maxR1,R2=R2, then R2R1 is equal to ______

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Show full solutionCorrect answer: 19
Correct answer
19

Step-by-step explanation

Intersection point of y2=x & y=2x in the first quadrant will be 14,12

Also, intersection point of y=x3 & y2=x in first quadrant will be 1,1

Area of the region S=∫01(x-x3)dx =2x323-x4410 =512

Area of region R1=∫014x-2xdx =2x323-x2014=148

∴  R2=S-R1=1948

So, R2R1=19

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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.