JEE Main 2022 · Mathematics · Area Under Curves · medium

If A is the area of the region bounded by the parabola y^2=4x and the line y=x, then 3A equals

Numerical answer

A

is the area of the region bounded by the parabola

y^2=4x

and the line

y=x

, then

3A

equals

Show answer and solution

Answer: 8

The curves meet where

x^2=4x

, i.e.

x=0

and

x=4

. Between them

y=2\sqrt x

lies above

y=x

, so

A=\int_0^4(2\sqrt x-x)\,dx=\left[\frac43x^{3/2}-\frac{x^2}2\right]_0^4=\frac{32}3-8=\frac83

. Hence

3A=8

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