JEE Main 2021MathematicsArea Under CurvesMediumNumerical

JEE Main 2021 — Area Under Curves Question with Solution

JEE Main 2021 (31 Aug Shift 2)

Question

If the line y=mx bisects the area enclosed by the lines x=0, y=0, x=32 and the curve y=1+4x-x2, then 12m is equal to            .

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Show full solutionCorrect answer: 26
Correct answer
26

Step-by-step explanation

Given, the equation of line, y=mx

And the line x=0, y=0, x=32 

The intersection point 32,0

Area of triangle is half the total area 

12∫03/21+4x-x2dx=∫03/2mxdx

12x+2x2-x3303/2=m2x203/2

32+92-98=9m4

398=9m4

m=3918

Then, 12m

12 m=3918×12

12m=26

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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.