5.3 The Fundamental Theorem of Calculus/19: Difference between revisions
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<math>\begin{align}\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]\end{align}</math> | <math>\begin{align}\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{align}</math> | ||
Revision as of 19:41, 25 August 2022
![{\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)