∫ − 1 2 ( x − 2 | x | ) d x = ∫ − 1 0 ( x − 2 ( − x ) ) d x + ∫ 0 2 ( x − 2 ( x ) ) d x = ( 1 2 x 2 + x 2 ) | − 1 0 + ( 1 2 x 2 − x 2 ) | 0 2 {\displaystyle {\begin{aligned}\int \limits _{-1}^{2}(x-2|x|)dx\\[1ex]&=\int \limits _{-1}^{0}(x-2(-x))dx+\int \limits _{0}^{2}(x-2(x))dx\\[2ex]&=\left({\frac {1}{2}}{x^{2}}+x^{2}\right){\bigg |}_{-1}^{0}+\left({\frac {1}{2}}{x^{2}}-x^{2}\right){\bigg |}_{0}^{2}\end{aligned}}}
![{\displaystyle {\begin{aligned}\int \limits _{-1}^{2}(x-2|x|)dx\\[1ex]&=\int \limits _{-1}^{0}(x-2(-x))dx+\int \limits _{0}^{2}(x-2(x))dx\\[2ex]&=\left({\frac {1}{2}}{x^{2}}+x^{2}\right){\bigg |}_{-1}^{0}+\left({\frac {1}{2}}{x^{2}}-x^{2}\right){\bigg |}_{0}^{2}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/10797d0980dd1f50259ad4dbf1931ba5377c1128)