Mathematics - Differential Equation Question with Solution | TestHub

The area of the region bounded by the curve $y=f(x)$ and the ordinates $x=a,x=b$ is given by $\text{Area }=\left|{\int }_a^{b}ydx\right|$ According to the question, $y=x|x|=\{\begin{array}{ll}{x}^2,& x\ge 0\\ -x^2,& x<0\end{array}$
Required area $=$ area of region $\mathrm{OAB}+$ area of region $\mathrm{OCD}$ $=2\times$ Area of region $\mathrm{OAB}$ $=2{\int }_0^1{x}^{2}dx=\frac{2}{3}sq$. units