5.3 The Fundamental Theorem of Calculus/8: Difference between revisions
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<math> g(x)=\int_{3}^{x}e^{t^2-t}dt </math> <br><br> | <math> g(x)=\int_{3}^{x}e^{t^2-t}dt </math> <br><br> | ||
<math>\frac{d}{dx}\left[g(x)\right] = \frac{d}{dx}\left[\int_{3}^{x}e^{t^2-t}dt\right]= | <math>\frac{d}{dx}\left[g(x)\right] = \frac{d}{dx}\left[\int_{3}^{x}e^{t^2-t}dt\right]=1\cdot(e^{x^2-x})-0\cdot(e^{3^2-3})=e^{x^2-x}</math> <br><br> | ||
<math>\text{Therefore, } g'(x)=e^{x^2-x}</math> | <math>\text{Therefore, } g'(x)=e^{x^2-x}</math> | ||
Revision as of 17:11, 25 August 2022
![{\displaystyle {\frac {d}{dx}}\left[g(x)\right]={\frac {d}{dx}}\left[\int _{3}^{x}e^{t^{2}-t}dt\right]=1\cdot (e^{x^{2}-x})-0\cdot (e^{3^{2}-3})=e^{x^{2}-x}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/67f74b496dc8f55f072918222a4f5a367ad16a8a)
