5.4 Indefinite Integrals and the Net Change Theorem/23: Difference between revisions
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<math> | <math> | ||
\begin{align} | \begin{align} | ||
\int_{-1}^{0}(2x-e^x)dx &=\left[\frac{2x^2}{2}-e^x\right] | \int_{-1}^{0}(2x-e^x)dx &=\left[\frac{2x^2}{2}-e^x\right]_{-1}^{0} \\[2ex] | ||
&= [0-e^{0}]-[(-1)^2-e^{-1}] \\[2ex] | &= [0^{2}-e^{0}]-[(-1)^2-e^{-1}] \\[2ex] | ||
&=-1-\left(1-\frac{1}{e}\right) \\[2ex] | &=-1-\left(1-\frac{1}{e}\right) \\[2ex] | ||
&=\frac{1}{e}-2 | &=\frac{1}{e}-2 | ||
Latest revision as of 19:40, 21 September 2022
![{\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)