Q. $\int_{- 1}^{1}{|1 - x|\ dx}$ is equal to
A) $- 2$
B) 0
C) 2
D) 4
Explanation
(c)
We have, $I = \int_{- 1}^{1}{|1 - x|dx}$
Here, $- 1 \leq x \leq 1\ \Rightarrow \ \ 1 - x \geq 0$
$\therefore\ I = \int_{- 1}^{1}{(1 - x)dx}$
$= \left\lbrack x - \frac{x^{2}}{2} \right\rbrack_{- 1}^{1} = 1 - \frac{1}{2} + 1 + \frac{1}{2} = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.