Math 22 Integration by Parts and Present Value - Revision history

Tphan046: /* Note */

2020-09-04T00:22:32Z

Note

2020-09-04T00:21:41Z

Integration by Parts

2020-08-18T14:18:12Z

Integration by Parts

2020-08-18T14:12:24Z

2020-08-18T14:10:36Z

2020-08-18T13:56:31Z

2020-08-17T15:32:46Z

Integration by Parts

2020-08-17T15:32:40Z

Integration by Parts

2020-08-17T15:32:05Z

2020-08-17T15:29:55Z

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← Older revision		Revision as of 00:22, 4 September 2020
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	==Note==		==Note==
−	1. Tabular ~~method~~ is convenient in some cases.	+	1. Tabular integration technique (look it up) is convenient in some cases.

← Older revision		Revision as of 00:21, 4 September 2020
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	\|}		\|}

−		+	==Note==
		+	1. Tabular method is convenient in some cases.

@@ Line 48: / Line 48: @@
 |-
 |Therefore, <math>\int x^2e^{-x}dx=-x^2e^{-x}-2xe^{-x}-e^{-x}+C</math>
 |}

@@ Line 50: / Line 50: @@
 |}
-'''4)''' <math>\int xe^{3x}dx</math>
+'''4)''' <math>\int \frac{1}{x(ln x)^3}dx</math>
 {| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
 !Solution: &nbsp;

@@ Line 26: / Line 26: @@
 |and <math>dv=e^{3x}dx</math> and <math>v=\frac{1}{3}e^{3x}</math>
 |-
-|Then, by integration by parts: <math>\int xe^{3x}dx=x\frac{1}{3}e^{3x} -\int\frac{1}{3}e^{3x} dx=x\frac{1}{3}e^{3x}-\frac{1}{9}e^{3x} </math>
+|Then, by integration by parts: <math>\int xe^{3x}dx=x\frac{1}{3}e^{3x} -\int\frac{1}{3}e^{3x} dx=x\frac{1}{3}e^{3x}-\frac{1}{9}e^{3x} +C </math>
 |}

← Older revision		Revision as of 13:56, 18 August 2020
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	<math>\int u dv=uv-\int v du</math>		<math>\int u dv=uv-\int v du</math>

		+	'''Exercises''' Use integration by parts to evaluation:
		+
		+	'''1)''' <math>\int \ln x dx</math>
		+	{\| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	!Solution:
		+	\|-
		+	\|Let <math>u=\ln x</math>, <math>>du=\frac{1}{x}dx</math>
		+	\|-
		+	\|and <math>dv=dx</math> and <math>v=x</math>
		+	\|-
		+	\|Then, by integration by parts: <math>\int \ln x dx=x\ln x-\int x\frac{1}{x}dx=x\ln x-\int dx=x\ln x -x +C</math>
		+	\|}
		+
		+	'''2)''' <math>\int xe^{3x}dx</math>
		+	{\| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	!Solution:
		+	\|-
		+	\|Let <math>u=x</math>, <math>du=dx</math>
		+	\|-
		+	\|and <math>dv=e^{3x}dx</math> and <math>v=\frac{1}{3}e^{3x}</math>
		+	\|-
		+	\|Then, by integration by parts: <math>\int xe^{3x}dx=x\frac{1}{3}e^{3x} -\int\frac{1}{3}e^{3x} dx=x\frac{1}{3}e^{3x}-\frac{1}{9}e^{3x} </math>
		+	\|}

← Older revision		Revision as of 15:32, 17 August 2020
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	Let <math>u</math> and <math>v</math> be differentiable functions of <math>x</math>.		Let <math>u</math> and <math>v</math> be differentiable functions of <math>x</math>.

−	<math>\int u \dv=uv-\int v \du</math>	+	<math>\int u dv=uv-\int v du</math>

← Older revision		Revision as of 15:32, 17 August 2020
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		+	==Integration by Parts==
		+
		+	Let <math>u</math> and <math>v</math> be differentiable functions of <math>x</math>.
		+
		+	<math>\int u dv=uv-\int v du</math>
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	'''This page were made by [[Contributors\|Tri Phan]]'''		'''This page were made by [[Contributors\|Tri Phan]]'''