Question

Integrate:

${\int }_{-3}^3\left|x\right|dx$ equals ?

• A. $0$
• B. $9/2$
• C. $6$
• D. $9$

Answer 1

The correct option is D $9$

$\left|x\right|=x$ when $x>0$

$=-x$ when $x<0$

$={\int }_{-3}^0-x\cdot dx+{\int }_0^{3}x\cdot dx$

$=-{\left[\frac{x^2}{2}\right]}_{-3}^0+{\left[\frac{x^2}{2}\right]}_0^3$

$=-[0-\frac{9}{2}]+\left[\frac{9}{2}\right]$

$=9$