Question

The area bounded by the curve $y=x\left|x\right|,x-axis$ and the ordinates $x=-1$ and $x=1$ is given by

• A. $0$square units
• B. $\frac{1}{3}$square units
• C. $\frac{2}{3}$square units
• D. $\frac{4}{3}$ square units

Answer 1

The correct option is C $\frac{2}{3}$square units

$y=x|x|=\{x^2:x\ge 0{-x}^2:x<0\}A=2{\int }_0^1{x}^{2}dxA=2{\left[\frac{{\left(x\right)}^3}{3}\right]}_0^1=\frac{2}{3}$