Question

Evaluate: $\stackrel{2}{\underset{0}{\int }}|1-x|dx$.

Answer 1

${\int }_0^1(1-x)dx+{\int }_1^2-(1-x)dx$

$\Rightarrow {(x-\frac{x^2}{2})}_0^1+{(-x+\frac{x^2}{2})}_1^2$

$\Rightarrow \frac{1}{2}+(0-(-1/2\left)\right)$

$\Rightarrow 1$