Question

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

• A. $15$ sq. units
• B. $19$ sq. units
• C. $18$ sq. units
• D. $20$ sq. units

Answer 1

Answer: (C)

The equation of curve is
$y=x|x|$ $=\{\begin{array}{ll}{x}^2,& \text{x≥0}\\ -x^2,& \text{x<0}\end{array}$

$\therefore$ Required area = 2(Area shaded in first quadrant)
$=2\underset{0}{\overset{3}{\int }}{x}^{2}dx=2\times {\left[\frac{x^3}{3}\right]}_0^3=2\times 9=18$ sq. units