5.3 The Fundamental Theorem of Calculus/8 - Revision history

Dvaezazizi@laalliance.org: Protected "5.3 The Fundamental Theorem of Calculus/8" ([Edit=Allow only administrators] (indefinite) [Move=Allow only administrators] (indefinite))

2022-09-06T20:14:43Z

Protected "5.3 The Fundamental Theorem of Calculus/8" ([Edit=Allow only administrators] (indefinite) [Move=Allow only administrators] (indefinite))

← Older revision	Revision as of 20:14, 6 September 2022
(No difference)

Dvaezazizi@laalliance.org at 19:48, 6 September 2022

2022-09-06T19:48:15Z

← Older revision		Revision as of 19:48, 6 September 2022
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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>

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

Juanr69976@students.laalliance.org at 19:28, 25 August 2022

2022-08-25T19:28:17Z

← Older revision		Revision as of 19:28, 25 August 2022
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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>

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

Dvaezazizi@laalliance.org at 17:11, 25 August 2022

2022-08-25T17:11:01Z

← Older revision		Revision as of 17:11, 25 August 2022
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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]=1e^{x^2-x}-0e^{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>

Dvaezazizi@laalliance.org at 20:38, 23 August 2022

2022-08-23T20:38:33Z

← Older revision		Revision as of 20:38, 23 August 2022
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	<math> g(x)=\int_{3}^{x}e^{t^2-t}dt </math> <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]=1e^{x^2-x}-0e^{3^2-3}=e^{x^2-x}</math> <br>		<math>\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}</math> <br><br>
	<math>\text{Therefore, } g'(x)=e^{x^2-x}</math>		<math>\text{Therefore, } g'(x)=e^{x^2-x}</math>

Dvaezazizi@laalliance.org at 20:38, 23 August 2022

2022-08-23T20:38:20Z

@@ Line 1: / Line 1: @@
 <math> g(x)=\int_{3}^{x}e^{t^2-t}dt </math> <br>
-<math>\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}</math>
+<math>\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}</math> <br>
 <math>\text{Therefore, } g'(x)=e^{x^2-x}</math>

Dvaezazizi@laalliance.org at 20:38, 23 August 2022

2022-08-23T20:38:08Z

← Older revision		Revision as of 20:38, 23 August 2022
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	<math> g(x)=\int_{3}^{x}e^{t^2-t}dt </math>		<math> g(x)=\int_{3}^{x}e^{t^2-t}dt </math> <br>
	\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}		<math>\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}</math>
	\text{Therefore, } g'(x)=e^{x^2-x}		<math>\text{Therefore, } g'(x)=e^{x^2-x}</math>

	\end{align}		\end{align}

Dvaezazizi@laalliance.org at 20:34, 23 August 2022

2022-08-23T20:34:42Z

← Older revision		Revision as of 20:34, 23 August 2022
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	<math> g(x)=\int_{3}^{x}e^{t^2-t}dt ~~\break~~</math>		<math> g(x)=\int_{3}^{x}e^{t^2-t}dt </math>
	\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}

Dvaezazizi@laalliance.org at 20:34, 23 August 2022

2022-08-23T20:34:34Z

← Older revision		Revision as of 20:34, 23 August 2022
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	<math>		<math> g(x)=\int_{3}^{x}e^{t^2-t}dt \break</math>
	~~\begin{align}~~		\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}
	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}		\text{Therefore, } g'(x)=e^{x^2-x}

Dvaezazizi@laalliance.org at 20:34, 23 August 2022

2022-08-23T20:34:01Z

← Older revision		Revision as of 20:34, 23 August 2022
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	\begin{align}		\begin{align}
	g(x)=\int_{3}^{x}e^{t^2-t}dt \\		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}

← Older revision		Revision as of 19:48, 6 September 2022
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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>

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

← Older revision		Revision as of 19:28, 25 August 2022
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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>

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