∫ − 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 ] = 3 4 {\displaystyle {\begin{aligned}\int _{-1}^{2}(x^{3}-2x)\,dx&={\frac {x^{4}}{4}}-{\frac {2x^{2}}{2}}{\Bigg |}_{-1}^{2}\\[2ex]&=\left[{\frac {(2)^{4}}{4}}-{\frac {2(2)^{2}}{2}}\right]-\left[{\frac {(-1)^{4}}{4}}-{\frac {2(-1)^{2}}{2}}\right]\\[2ex]&=[0]-\left[{\frac {1}{4}}-1\right]\\[2ex]&={\frac {3}{4}}\end{aligned}}}
![{\displaystyle {\begin{aligned}\int _{-1}^{2}(x^{3}-2x)\,dx&={\frac {x^{4}}{4}}-{\frac {2x^{2}}{2}}{\Bigg |}_{-1}^{2}\\[2ex]&=\left[{\frac {(2)^{4}}{4}}-{\frac {2(2)^{2}}{2}}\right]-\left[{\frac {(-1)^{4}}{4}}-{\frac {2(-1)^{2}}{2}}\right]\\[2ex]&=[0]-\left[{\frac {1}{4}}-1\right]\\[2ex]&={\frac {3}{4}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/1450c8696d7f5791e5cb8781b0593862d42b8b75)