Question

If $0<a<b$, then $\stackrel{b}{\underset{a}{\int }}\frac{|x|}{x}dx$ is equal to

• A. $|b|-|a|$
• B. $|a|-|b|$
• C. $\frac{|b|}{|a|}$
• D. $0$

Answer 1

The correct option is A $|b|-|a|$

Solution:

$\stackrel{b}{\underset{a}{\int }}\frac{|x|}{x}dx=\stackrel{b}{\underset{a}{\int }}1dx$ $[\because 0<a<b]$

$=[x{]}_a^b=|b|-|a|$

Hence, A is the correct option.