Question

Evaluate: ${\int }_{-1}^1\frac{|x+2|}{x+2}dx$

• A. $1$
• B. $2$
• C. $0$
• D. $-1$

Answer 1

The correct option is B $2$

We know that $|f\left(x\right)|=f\left(x\right)$ for $f\left(x\right)\ge 0$ and $|f\left(x\right)|=-f\left(x\right)$ for $f\left(x\right)<0$

Here, $|x+2|>0\forall x\in [-1,1]$

Hence, $|x+2|=x+2$

Hence, integration becomes:-

${\int }_{-1}^{1}1.dx$

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

$=2$

Hence, answer is option-(B).