Question

Let the area of the region \left\\{(x, y):|2 x-1| \leq y \leq\left|x^2-x\right|, 0 \leq x \leq 1\right\\} be $A$ Then $(6 A +11)^2$ is equal to ____

Answer 1

The correct answer is 125.
y≥∣2x−1∣,y≤∣∣​x2−x∣∣​

Both curve are symmetric about x=21​ Hence
A=223−5​​∫21​​((x−x2)−(1−2x))dx
A=223−5​​∫21​​(−x2+3x−1)dx=2(3−x3​+23​x2−x)23−5​​21​​
On solving 6A+11=55​
(6A+11)2=125