∫ − 1 2 ( x 3 − 2 x ) d x = x 4 4 − 2 x 2 2 | − 1 2 = ( 2 ) 4 4 − 2 ( 2 ) 2 2 − [ ( − 1 ) 4 4 − 2 ( − 1 ) 2 2 ] = 0 − [ 1 4 − 1 ] {\displaystyle {\begin{aligned}\int _{-1}^{2}(x^{3}-2x)dx&={\frac {x^{4}}{4}}-{\frac {2x^{2}}{2}}{\Bigg |}_{-1}^{2}\\[2ex]&={\frac {(2)^{4}}{4}}-{\frac {2(2)^{2}}{2}}-\left[{\frac {(-1)^{4}}{4}}-{\frac {2(-1)^{2}}{2}}\right]\\[2ex]&=0-\left[{\frac {1}{4}}-1\right]\end{aligned}}}
![{\displaystyle {\begin{aligned}\int _{-1}^{2}(x^{3}-2x)dx&={\frac {x^{4}}{4}}-{\frac {2x^{2}}{2}}{\Bigg |}_{-1}^{2}\\[2ex]&={\frac {(2)^{4}}{4}}-{\frac {2(2)^{2}}{2}}-\left[{\frac {(-1)^{4}}{4}}-{\frac {2(-1)^{2}}{2}}\right]\\[2ex]&=0-\left[{\frac {1}{4}}-1\right]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/9b14e75c485cadc3e4189efec42429c077880723)