Question

The value of ${\int }_{-1}^3(|x|+|x-1|)dx$, is equal to

• A. $9$
• B. $6$
• C. $3$
• D. none of these

Answer 1

The correct option is A $9$

${\int }_{-1}^3(|x|+|x-1|)dx$
$={\int }_{-1}^3|x|dx+{\int }_{-1}^3|x-1|dx$
$={\int }_{-1}^0(-x)dx+{\int }_0^3\left(x\right)dx+{\int }_{-1}^1(-x+1)dx+{\int }_1^3(x-1)dx$
$=[-\frac{x^2}{2}{]}_{-1}^0+[\frac{x^2}{2}{]}_0^3+[-\frac{x^2}{2}+x{]}_{-1}^1+[\frac{x^2}{2}-x{]}_1^3$
$\Rightarrow I=9$