Question

$\underset{-5}{\overset{5}{\int }}|x+2|dx$ is equal to

• A. $29$
• B. $28$
• C. $27$
• D. $30$

Answer 1

The correct option is A $29$

We know that $f\left(x\right)=\{\begin{array}{c}-(x+2)\text{if}x<-2\\ x+2\text{if}x\ge -2\end{array}$

$\underset{-5}{\overset{5}{\int }}|x+2|dx=\underset{-5}{\overset{-2}{\int }}(-x-2)dx+\underset{-2}{\overset{5}{\int }}(x+2)dx$

$={[-\frac{x^2}{2}-2x]}_{-5}^{-2}+{\left[\frac{x^2}{2}+2x\right]}_{-2}^5$

$=\frac{9}{2}+\frac{49}{2}=29$