Question

1. Find the area between the curves y= x^2-3x and y=x.

Answer 1

First let's find the intersection points of these curves

$x^2-3x=x\iff x^2-4x=0$

$x=0;\quad x=4$

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

$S=\left|\int\limits_0^4(x^2-4x)dx\right|=\left|\left(\frac{x^3}{3}-2x^2\right)_0^4\right|=\left| \frac{64}{3}-32\right|=\frac{32}{3}$