Question

The value of ${\int }_{-1}^2\frac{|x|}{x}dx$ is?

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

$1$

${\int }_{-1}^2\frac{|x|}{x}dx={\int }_{-1}^0\frac{|x|}{x}dx+{\int }_0^2\frac{|x|}{x}dx$

$={\int }_{-1}^0\frac{-x}{x}dx+{\int }_0^2\frac{x}{x}dx$

$=-1{\int }_{-1}^{0}dx+{\int }_0^{2}dx$

$=-1(0+1)+1(2-0)=-1+2=1$