Discussion Forum

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

Answer:

Explanation:

We have,

 $x=y^{2}-2$ and x=y

 Graph of $x=y^{2}-2$ and x=y are 

 Solving, $x=y^{2}-2$  and x=y , we get (-1,-1) and (2,2) 

Area of shaded region is 

$\int_{-1}^{2} ydy-\int_{-1}^{2} (y^{2}-2)dy$

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

                           $\left(\frac{4}{2}-\frac{8}{3}+4\right)-\left(\frac{1}{2}+\frac{1}{3}-2\right)$

   = $\frac{10}{3}+\frac{7}{6}=\frac{27}{6}=\frac{9}{2}$