Q. $\int_{a}^{b}{\frac{|x|}{x}dx,\ a < 0 < b,}$is equal to
A) $|b| - |a|$
B) $|b| + |a|$
C) $|a - b|$
D) None of these
Explanation
(a)
$\int_{a}^{b}{\frac{|x|}{x}dx = \int_{a}^{0}\frac{|x|}{x}dx + \int_{0}^{b}\frac{|x|}{x}dx\ \ \ \lbrack\because a < 0 < b\rbrack}$
$= \int_{a}^{0}{- 1\ dx + \int_{0}^{b}{1\ dx}}$
$= a + b = b - ( - a)|b| - |a|$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.