Mathematics - Area Under Curves Question with Solution | TestHub

$\begin{array}{rl}& \text{ Shaded area }={\int }_{-\frac{1}{2}}^1\left(x_{\text{Right }}-x_{\text{Left }}\right)dy\\ & y^2=2x\\ & y=4x-1\text{ Solve }\\ & y=1,y=-\frac{1}{2}\\ & \text{ Shaded area }={\int }_{-\frac{1}{2}}^1\left(\frac{y+1}{4}-\frac{y^2}{2}\right)dy\\ & ={\left(\frac{1}{4}\left(\frac{y^2}{2}+y\right)-\frac{y^3}{6}\right)}_{-\frac{1}{2}}^1=\frac{9}{32}\end{array}$