Question

The value of integral $\int\limits_{-1}^{1} \frac{\left|x+2\right|}{x+2} dx$ is

• A. $1$
• B. $2$
• C. $0$
• D. $-1$

Answer 1

Answer: (B)

Let $I=\int\limits_{-1}^{1} \frac{\left|x+2\right|}{x+2}dx$

For $-1\le\,x\, \le\,1, \left|x+2\right|=2+x$

$\therefore \, I=\int\limits_{-1}^{1} \frac{x+2}{x+2}dx$

$=\int\limits_{-1}^{1}1\,dx$

$=\left[x\right]_{-1}^{1}=1-\left(-1\right)$

$=2$