Q. $\int_{}^{}{|x|dx}$ is equal to
A) $\frac{1}{2}x^{2} + c$
B) $- \frac{x^{2}}{2} + c$
C) $x|x| + c$
D) $\frac{1}{2}x|x| + c$
Explanation
(d)
Let $I = \int_{}^{}{|x| \bullet 1dx}$
$= |x|x - \int_{}^{}{\frac{|x|}{x}x\ dx = x|x| - \int_{}^{}{|x|dx}}$
$\Rightarrow 2I = x|x|$
$\Rightarrow I = \frac{x|x|}{2} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.