Question

$\underset{-1}{\overset{1}{\int }}\left|1-x\right|dx$ is equal to

(a) −2
(b) 2
(c) 0
(d) 4

Answer 1

(b) 2

$$\begin{gathered} {\int }_{-1}^1\left|1-x\right|dx \\ ={\int }_{-1}^0\left(1-x\right)dx+{\int }_0^1\left(1-x\right)dx \\ ={\left[x-\frac{x^2}{2}\right]}_{-1}^0+{\left[x-\frac{x^2}{2}\right]}_0^1 \\ =0+1+\frac{1}{2}+1-\frac{1}{2}-0 \\ =2 \end{gathered}$$