Question

Find the area bounded by the curve $y=x|x|$, X-axis and the ordinates $x=-3$ and $x=3$.

• A. $9$ sq. units
  
• B. $18$ sq. units
  
• C. $27$ sq. units
  
• D. $81$ sq. units
  

Answer 1

The correct option is B $18$ sq. units

$y=\mid x\mid$$=\{x^2;x\ge 0-x^2;x<0\}$

$A=2{\int }_0^3{x}^{2}dxA={2\left[\frac{x^3}{3}\right]}_0^3$

$A=2\left(\frac{3^3}{3}\right)$

$A=2\times 9=18squnits$