Question

The value of ${\int }_a^b\frac{x}{|x|}dx,a<b<0$ is

• A. $-(|a|+|b|)$
• B. $|b|-|a|$
• C. $|a|-|b|$
• D. $|a|+|b|$

Answer 1

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

$\int \frac{x}{|x|}dx$

$=|x|+C$

${\int }_a^b\frac{x}{|x|}dx$

$={\left[|x|\right]}_a^b$

$=|b|-|a|$