Mathematics - Area Under Curves Question with Solution | TestHub

Hints: $y=4x^2$ $$y=\frac{x^2}{4}$$ $$\begin{array}{rl}& A={\int }_{\mathrm{r}}^2\left[\frac{\sqrt{y}}{2}-3\sqrt{y}\right]dy=\left(\frac{1}{2}-3\right){\int }_0^2\sqrt{y}dy\\ & =\left(\frac{-\sqrt{\mathrm{y}}}{2}\right)\frac{5}{3}{\left({\mathrm{y}}^{3/2}\right)}_0^2=-\frac{5}{3}(2\sqrt{2}-0)\\ & =\left|-\frac{\sqrt{2}}{3}\right|=\frac{10\sqrt{2}}{3}\text{, Area of bounded figure }=2\mathrm{A}=\frac{20\sqrt{2}}{3}\\ & \end{array}$$