Mathematics Question on Area between Two Curves

Question

Let $A$ be the area of the region
$\left\\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\\}$ .
Then $540 A$ is equal to ______.

Accepted Answer

area of the region

A=231∫21(2x−2x2−(1−x)2)dx
=2[2x2−x3−x]1/31/2
∴A=1085⇒540A=1085×540=25
So , the correct answer is 25.