1. Tardigrade
  2. Question
  3. Mathematics
  4. Find the area bounded by the curve y = x|x|, x-axis and the lines x = -3 and x = 3.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Application of Integrals

Solution:

The equation of curve is
$y=x|x|$ $ = \begin{cases} x^{2}, & \text{$x \ge\,0$} \\[2ex] -x^{2}, & \text{$x <\, 0$} \end{cases}$
image
$\therefore \quad$ Required area = 2(Area shaded in first quadrant)
$=2\int\limits_{0}^{3} x^{2} \, dx=2\times\left[\frac{x^{3}}{3}\right]_{0}^{3}=2\times9=18$ sq. units