Q. The value of the integral $\int_{0}^{2}{|x^{2} - 1|dx}\$is
A) 0
B) 2
C) $- \frac{1}{3}$
D) $- 2$
Explanation
(b)
$\int_{0}^{2}{\left| x^{2} - 1 \right|dx = \int_{0}^{1}{- \left( x^{2} - 1 \right)dx + \int_{1}^{2}{\left( x^{2} - 1 \right)dx}}}$
$= \left\lbrack - \frac{x^{3}}{3} + x \right\rbrack_{0}^{1} + \left\lbrack \frac{x^{3}}{3} - x \right\rbrack_{1}^{2}$
$= - \frac{1}{3} + 1 + \frac{8}{3} - 2 - \frac{1}{3} + 1$
=2
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.