7.1 Integration By Parts/32 - Revision history

Dvaezazizi@laalliance.org at 17:06, 29 November 2022

2022-11-29T17:06:13Z

← Older revision		Revision as of 17:06, 29 November 2022
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	<math>\int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - \int_{0}^{t} e^s \cos(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - e^s \cdot \sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds</math><br>		<math>\int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - \int_{0}^{t} e^s \cos(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - e^s \cdot \sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds</math><br>

	<math> u= e^s ~ ~ ~ ~ ~ dv=\sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=\cos(t-s)</math><br>		<math> u= e^s ~ ~ ~ ~ ~ dv=\sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=\cos(t-s)</math><br>

	<math>du= e^s ds~ ~ v=\cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-\sin(t-s)</math> <br><br>		<math>du= e^s ds~ ~ v=\cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-\sin(t-s)</math> <br><br>

Dvaezazizi@laalliance.org at 17:05, 29 November 2022

2022-11-29T17:05:59Z

← Older revision		Revision as of 17:05, 29 November 2022
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	<math>\int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - \int_{0}^{t} e^s \cos(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - e^s \cdot \sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds</math><br>		<math>\int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - \int_{0}^{t} e^s \cos(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - e^s \cdot \sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds</math><br>

	<math> u= e^s ~ ~ ~ ~ ~ dv=\sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=\cos(t-s)</math><br>		<math> u= e^s ~ ~ ~ ~ ~ dv=\sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=\cos(t-s)</math><br>

	<math>du= e^s ds~ ~ v=\cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-\sin(t-s)</math> <br><br>		<math>du= e^s ds~ ~ v=\cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-\sin(t-s)</math> <br><br>

Juanr69976@students.laalliance.org at 02:34, 27 November 2022

2022-11-27T02:34:40Z

← Older revision		Revision as of 02:34, 27 November 2022
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	<math> f'(x)= \int_{0}^{t} e^s sin(t-s) \cdot ds </math> <br><br>		<math> f'(x)= \int_{0}^{t} e^s sin(t-s) \cdot ds </math> <br><br>

	<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - \int_{0}^{t} e^s cos(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - e^s \cdot sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds</math><br>		<math>\int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - \int_{0}^{t} e^s \cos(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - e^s \cdot \sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds</math><br>

	<math> u= e^s ~ ~ ~ ~ ~ dv=sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=cos(t-s)</math><br>		<math> u= e^s ~ ~ ~ ~ ~ dv=\sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=\cos(t-s)</math><br>

	<math>du= e^s ds~ ~ v=cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-sin(t-s)</math> <br><br>		<math>du= e^s ds~ ~ v=\cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-\sin(t-s)</math> <br><br>

	<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - e^s \cdot sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds</math><br>		<math>\int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - e^s \cdot \sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds</math><br>

	<math>2\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - e^s \cdot sin(t-s)</math><br>		<math>2\int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - e^s \cdot \sin(t-s)</math><br>

	<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ \frac{e^s}{2}(cos(t-s) - sin(t-s)) \Bigg\|_0^t</math><br>		<math>\int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ \frac{e^s}{2}(\cos(t-s) - \sin(t-s)) \Bigg\|_0^t</math><br>

	<math>=\frac{e^t}{2}(cos(0) - sin(0)) -\frac{e^0}{2}(cos(t) - sin(t))</math><br>		<math>=\frac{e^t}{2}(\cos(0) - \sin(0)) -\frac{e^0}{2}(\cos(t) - \sin(t))</math><br>

	<math>=\frac{e^t}{2}-\frac{1}{2}(cos(t) - sin(t))</math><br>		<math>=\frac{e^t}{2}-\frac{1}{2}(\cos(t) - \sin(t))</math><br>

	[[7.1 Integration By Parts/1\|1]]		[[7.1 Integration By Parts/1\|1]]

Juanr69976@students.laalliance.org at 02:33, 27 November 2022

2022-11-27T02:33:01Z

← Older revision		Revision as of 02:33, 27 November 2022
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	<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ \frac{e^s}{2}(cos(t-s) - sin(t-s)) \Bigg\|_0^t</math><br>		<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ \frac{e^s}{2}(cos(t-s) - sin(t-s)) \Bigg\|_0^t</math><br>

	<math>=\frac{e^s}{2}(cos(0) - sin(0)) -\frac{e^s}{2}(cos(t) - sin(t))</math><br>		<math>=\frac{e^t}{2}(cos(0) - sin(0)) -\frac{e^0}{2}(cos(t) - sin(t))</math><br>

			<math>=\frac{e^t}{2}-\frac{1}{2}(cos(t) - sin(t))</math><br>

	[[7.1 Integration By Parts/1\|1]]		[[7.1 Integration By Parts/1\|1]]

Juanr69976@students.laalliance.org at 02:27, 27 November 2022

2022-11-27T02:27:06Z

← Older revision		Revision as of 02:27, 27 November 2022
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	<math> f'(x)= \int_{0}^{t} e^s sin(t-s) \cdot ds </math> <br><br>		<math> f'(x)= \int_{0}^{t} e^s sin(t-s) \cdot ds </math> <br><br>

	<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - \int_{0}^{t} e^s cos(t-s) \cdot ds</math><br>		<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - \int_{0}^{t} e^s cos(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - e^s \cdot sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds</math><br>

	<math> u= e^s ~ ~ ~ ~ ~ dv=sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=cos(t-s)</math><br>		<math> u= e^s ~ ~ ~ ~ ~ dv=sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=cos(t-s)</math><br>
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	<math>du= e^s ds~ ~ v=cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-sin(t-s)</math> <br><br>		<math>du= e^s ds~ ~ v=cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-sin(t-s)</math> <br><br>

	<math>=\~~frac~~{32}{5} (\ln(2))^2 -\~~frac~~{64}{25} (\ln(2)) + \~~frac{62}{125}~~</math>		<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - e^s \cdot sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds</math><br>

			<math>2\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - e^s \cdot sin(t-s)</math><br>

			<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ \frac{e^s}{2}(cos(t-s) - sin(t-s)) \Bigg\|_0^t</math><br>

			<math>=\frac{e^s}{2}(cos(0) - sin(0)) -\frac{e^s}{2}(cos(t) - sin(t))</math><br>

	[[7.1 Integration By Parts/1\|1]]		[[7.1 Integration By Parts/1\|1]]

Juanr69976@students.laalliance.org: Created page with " $f'(x)= \int_{0}^{t} e^s sin(t-s) \cdot ds$

$\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - \int_{0}^{t} e^s cos(t-s) \cdot ds$
$u= e^s ~ ~ ~ ~ ~ dv=sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=cos(t-s)$
$du= e^s ds~ ~ v=cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-sin(t-s)$

$=\frac{32}{5} (\ln(2))^2 -\frac{64}{25} (\ln(2)) + \fr..."$

2022-11-27T01:24:13Z

Created page with "<math> f'(x)= \int_{0}^{t} e^s sin(t-s) \cdot ds </math> <math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - \int_{0}^{t} e^s cos(t-s) \cdot ds</math> <math> u= e^s ~ ~ ~ ~ ~ dv=sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=cos(t-s)</math> <math>du= e^s ds~ ~ v=cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-sin(t-s)</math> <math>=\frac{32}{5} (\ln(2))^2 -\frac{64}{25} (\ln(2)) + \fr..."

New page

<math> f'(x)= \int_{0}^{t} e^s sin(t-s) \cdot ds </math> 

<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - \int_{0}^{t} e^s cos(t-s) \cdot ds</math> 

<math> u= e^s ~ ~ ~ ~ ~ dv=sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=cos(t-s)</math> 

<math>du= e^s ds~ ~ v=cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-sin(t-s)</math> 

<math>=\frac{32}{5} (\ln(2))^2 -\frac{64}{25} (\ln(2)) + \frac{62}{125}</math>

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