Question

Find the area bounded by the curve, $y=x\left|x\right|$, x-axis and the ordinates $x=-\frac{1}{2}$ and $x=1$:

• A. $\frac{13}{24}sq.units$
• B. $\frac{17}{24}sq.units$
• C. $\frac{11}{24}sq.units$
• D. None of these
  

Answer 1

The correct option is D None of these

Area bounded
$={\int }_{-1/2}^0-x^{2}dx+{\int }_0^1{x}^{2}dx$
$=\frac{-x^3}{3}{|}_{-1/2}^0+\frac{x^3}{3}{|}_0^1$
$=\frac{3}{8}$