5.3 The Fundamental Theorem of Calculus/19: Difference between revisions
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<math> | <math> | ||
\begin{align}\int_{-1}^{2}(x^3-2x)dx &= \frac{x^4}{4}-\frac{2x^2}{2}\Bigg|_{-1}^{2}\\[2ex] | \begin{align}\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] | &=\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]=\frac{3}{4} | &=[0]-\left[\frac{1}{4}-1\right] \\[2ex] | ||
&=\frac{3}{4} | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 20:36, 6 September 2022
![{\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)