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| <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>\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> |
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| [[5.3 The Fundamental Theorem of Calculus/1|1]]
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| [[5.3 The Fundamental Theorem of Calculus/3|3]]
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| [[5.3 The Fundamental Theorem of Calculus/5|5]]
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| [[5.3 The Fundamental Theorem of Calculus/7|7]]
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| [[5.3 The Fundamental Theorem of Calculus/8|8]]
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| [[5.3 The Fundamental Theorem of Calculus/9|9]]
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| [[5.3 The Fundamental Theorem of Calculus/10|10]]
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| [[5.3 The Fundamental Theorem of Calculus/11|11]]
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| [[5.3 The Fundamental Theorem of Calculus/13|13]]
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| [[5.3 The Fundamental Theorem of Calculus/15|15]]
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| [[5.3 The Fundamental Theorem of Calculus/17|17]]
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| [[5.3 The Fundamental Theorem of Calculus/19|19]]
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| [[5.3 The Fundamental Theorem of Calculus/20|20]]
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| [[5.3 The Fundamental Theorem of Calculus/21|21]]
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| [[5.3 The Fundamental Theorem of Calculus/23|23]]
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| [[5.3 The Fundamental Theorem of Calculus/25|25]]
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| [[5.3 The Fundamental Theorem of Calculus/27|27]]
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| [[5.3 The Fundamental Theorem of Calculus/28|28]]
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| [[5.3 The Fundamental Theorem of Calculus/29|29]]
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| [[5.3 The Fundamental Theorem of Calculus/31|31]]
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| [[5.3 The Fundamental Theorem of Calculus/33|33]]
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| [[5.3 The Fundamental Theorem of Calculus/35|35]]
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| [[5.3 The Fundamental Theorem of Calculus/37|37]]
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| [[5.3 The Fundamental Theorem of Calculus/39|39]]
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| [[5.3 The Fundamental Theorem of Calculus/41|41]]
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| [[5.3 The Fundamental Theorem of Calculus/53|53]]
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![{\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)
