Question

The area of the region bounded by the curve $x=y^2-2$ and $x=y$ is

• A. $\frac{9}{4}$
• B. $9$
• C. $\frac{9}{2}$
• D. $\frac{9}{7}$

Answer 1

Answer: (C)

$\frac{9}{2}$

To find the Area of the region bounded by the curve

$x=y^2-2$ and $x=y$

First , we have to find the point of Intersection of the 2 curves

$y=y^2-2$

$y^2-y-2=0$

$(y-2)(y+1)=0$

$y=-1,y=2$

Now , Area of the region bounded by the curve is

${\int }_{y=-1}^2[y-(y^2-2\left)\right]dy$

${\int }_{y=-1}^2[y-y^2+2]dy$

$={[-\frac{y^3}{3}+\frac{y^2}{2}+2y]}_{y=-1}^2$

$=\frac{9}{2}$