Question

If the area of the region bounded by the curves $y ^2-2 y=-x, x+y=0$ is $A$, then $8 A$ is equal to _________

Answer 1

The correct answer is 36
y2−2y=−x
⇒y2−2y+1=−x+1
(y−1)2=−(x−1)
y=−x
Points of intersection
x2+2x=−x
x2+3x=0
x=0,−3

A=0∫3​(−y2+2y+y)dy
=23y2​−3y3​∣∣​03​=29​
8A=36