Mathematics - Area Under Curves Question with Solution | TestHub

$y=x^2-5x$ and $y=7x-x^2$
$\begin{array}{rl}& {\int }_0^6(g(x)-f(x))dx\\ & {\int }_0^6\left(\left(7x-x^2\right)-\left(x^2-5x\right)\right)dx\\ & {\int }_0^6\left(12x-2x^2\right)dx={\left[12\frac{x^2}{2}-\frac{2x^3}{3}\right]}_0^6\\ & \Rightarrow 6(6{)}^2-\frac{2}{3}(6{)}^3\\ & =216-144=72{\text{ unit }}^2\\ & \end{array}$