Question

Find the area enclosed by $y=x|x|,y=0,x=1,y=-1$

Answer 1

$\begin{array}{c}y=x^{2}x>0\\ y=-x^{2}x<0\\ \Rightarrow -{\int }_{-1}^0\sqrt{-y}+{\int }_0^1{x}^2\\ \Rightarrow -{\left[\frac{{\left(-y\right)}^{3/2}}{3/2}\right]}_{-1}^0+{\left[\frac{x^3}{3}\right]}_0^1\\ \Rightarrow \frac{-2}{3}\left[0-1\right]+3\left[1-0\right]=\frac{2}{3}+3=\frac{11}{3}sq.unit\end{array}$