5.3 The Fundamental Theorem of Calculus/8: Difference between revisions
Jump to navigation
Jump to search
No edit summary Tag: Manual revert |
No edit summary |
||
| Line 1: | Line 1: | ||
<math>g(x)=\int_{3}^{x}e^{t^2-t}dt | <math>g(x)=\int_{3}^{x}e^{t^2-t}dt // | ||
\frac{d}{dx}\left[g(x)\right] = \frac{d}{dx}\left[\int_{3}^{x}e^{t^2-t}dt\right]=1e^{x^2-x}-0e^{3^2-3}=e^{x^2-x} | \frac{d}{dx}\left[g(x)\right] = \frac{d}{dx}\left[\int_{3}^{x}e^{t^2-t}dt\right]=1e^{x^2-x}-0e^{3^2-3}=e^{x^2-x} | ||
\text{Therefore, } g'(x)=e^{x^2-x} | \text{Therefore, } g'(x)=e^{x^2-x} | ||
</math> | </math> | ||
Revision as of 20:27, 23 August 2022
![{\displaystyle g(x)=\int _{3}^{x}e^{t^{2}-t}dt//{\frac {d}{dx}}\left[g(x)\right]={\frac {d}{dx}}\left[\int _{3}^{x}e^{t^{2}-t}dt\right]=1e^{x^{2}-x}-0e^{3^{2}-3}=e^{x^{2}-x}{\text{Therefore, }}g'(x)=e^{x^{2}-x}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/64ec10d4bded37aa11aa62dc7b51e458b51ab718)