Question

The integral $\underset{0}{\overset{2}{\int }}\Vert x-1|-x|dx$ is equal to ______.

Answer 1

Answer: 1.50

$\underset{0}{\overset{2}{\int }}|x-1|-x\mid dx$
Let $f(x)\Vert x-1|-x|=\{\begin{array}{ll}1,& x\ge 1\\ |1-2x|,& x\le 1\end{array}$

$A=\frac{1}{2}+1=\frac{3}{2}$
Or
$\underset{0}{\overset{1/2}{\int }}(1-2x)dx+\underset{1/2}{\overset{1}{\int }}(2x-1)+\underset{0}{\overset{2}{\int }}1dx$
$={\left[x-x^2\right]}_0^{\frac{1}{2}}+{\left[x^2-x\right]}_{1/2}^1+[x{]}_1^2$
$=3/2$