Question

The value of integral ${\int }_{-1}^1\left[\frac{\left|x+2\right|}{(x+2)}\right]dx=$

• A. $1$
• B. $2$
• C. $0$
• D. $-1$

Answer 1

The correct option is B

$2$

Explanation for the correct option

Given: ${\int }_{-1}^1\left[\frac{\left|x+2\right|}{(x+2)}\right]dx$

Let ${\int }_{-1}^1\left[\frac{\left|x+2\right|}{(x+2)}\right]dx=I$

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

$$\begin{gathered} I={\int }_{-1}^1\left[\frac{\left(x+2\right)}{(x+2)}\right]dx \\ \Rightarrow I={\int }_{-1}^1\left[1\right]dx \\ \Rightarrow I={\left|x\right|}_{-1}^1 \\ \Rightarrow I=\left|1-(-1)\right| \\ \Rightarrow I=2 \end{gathered}$$

Hence, option B is correct.