The area enclosed by the curves $y=x|x|$, $x=-1$ and $x=1$ is.......... sq units.

Question

Aicharya · Accepted Answer

Given, curves are $y=x|x|=\left\{\begin{array}{cc}x^2 & ; \quad x \geq 0 \\ -x^2 & ; \quad x < 0\end{array}\right.$ $x=-1$ and $x=1$

We have plotted the figure and shaded regions are the area enclosed by the curves and area of 1 first part $=$ Area of II second part. $A_1=\int_0^1 x^2 d x=\left[\frac{x^3}{3}\right]_0^1=\frac{1}{3}$ Similarly, $A_{11}=\frac{1}{3}$ $\therefore \quad A=\frac{1}{3}+\frac{1}{3}=\frac{2}{3}$

The area enclosed by the curves $y=x|x|$, $x=-1$ and $x=1$ is.......... sq units.

Solution