Question

1. Find the area of the regionenclosed by the curves x=y^2-2 and x=y.

Answer 1

First let's find the intersection points of these curves

$y^2-2=y\iff y^2-2-y=0$

$y=-1;\quad y=2$

The area between these curves can be found as a Riemann integral

$S=\left|\int\limits_{-1}^2(y^2-y-2)dy\right|=\left|\left(\frac{y^3}{3}-\frac{y^2}{2}-2y\right)_{-1}^2\right|=\frac{9}{2}$