다음 적분을 구하라.
$$\int_{-1}^2\vert x-1\vert dx$$
풀이
\(\displaystyle\int_{-1}^2\vert x-1\vert dx=\int_1^2(x-1)dx+\int_{-1}^1(-x+1)dx\)
\(\displaystyle=\left[\frac{1}{2}x^2-x\right]_1^2+\left[-\frac{1}{2}x^2+x\right]_{-1}^1\)
\(\displaystyle=\frac{2^2}{2}-2-\left(\frac{1^2}{2}-1\right)-\frac{1^2}{2}+1-\left(-\frac{(-1)^2}{2}-1\right)\)
\(\displaystyle=0-\left(-\frac{1}{2}\right)+\frac{1}{2}-\left(-\frac{3}{2}\right)=\frac{5}{2}\)