∫ − 1 0 ( 2 x − e x ) d x = [ 2 x 2 2 − e x ] − 1 0 = [ 0 2 − e 0 ] − [ ( − 1 ) 2 − e − 1 ] = − 1 − ( 1 − 1 e ) = 1 e − 2 {\displaystyle {\begin{aligned}\int _{-1}^{0}(2x-e^{x})dx&=\left[{\frac {2x^{2}}{2}}-e^{x}\right]_{-1}^{0}\\[2ex]&=[0^{2}-e^{0}]-[(-1)^{2}-e^{-1}]\\[2ex]&=-1-\left(1-{\frac {1}{e}}\right)\\[2ex]&={\frac {1}{e}}-2\end{aligned}}}
![{\displaystyle {\begin{aligned}\int _{-1}^{0}(2x-e^{x})dx&=\left[{\frac {2x^{2}}{2}}-e^{x}\right]_{-1}^{0}\\[2ex]&=[0^{2}-e^{0}]-[(-1)^{2}-e^{-1}]\\[2ex]&=-1-\left(1-{\frac {1}{e}}\right)\\[2ex]&={\frac {1}{e}}-2\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/a6a9f752e7d5f4926a1d9d37c1b83eac0662b7b4)