C4 Integration - Revision history

IDI: /* Homework */

2014-01-08T14:27:50Z

‎Homework

IDI: /* Integration 'flowchart' */

2014-01-08T13:05:17Z

‎Integration 'flowchart'

IDI: /* Integration 'flowchart' */

2014-01-08T13:03:59Z

‎Integration 'flowchart'

IDI: /* Integration 'flowchart' */

2014-01-08T13:01:34Z

‎Integration 'flowchart'

IDI: /* Integration 'flowchart' */

2014-01-08T13:00:53Z

‎Integration 'flowchart'

IDI: /* Integration 'flowchart' */

2014-01-08T13:00:10Z

‎Integration 'flowchart'

IDI: /* Notes */

2014-01-08T12:55:45Z

‎Notes

IDI: /* Objectives */

2014-01-08T12:31:41Z

‎Objectives

Ian: Created page with "Part of C4 == Objectives == Integration of $e^x$ , $\frac{1}{x}$ , $\sin{x}<\math>, \cos{x}<\math> Evaluation of volume of r..."$

2013-09-03T22:22:46Z

Created page with "Part of C4 == Objectives == <onlyinclude> *Integration of <math>e^x</math>, <math>\frac{1}{x}</math>, <math>\sin{x}<\math>, <math>\cos{x}<\math> *Evaluation of volume of r..."

New page

Part of [[C4]]
== Objectives ==
<onlyinclude>
*Integration of <math>e^x</math>, <math>\frac{1}{x}</math>, <math>\sin{x}<\math>, <math>\cos{x}<\math>
*Evaluation of volume of revolution
*Simple cases of integration by substitution and integration by parts. These methods as the reverse processes of the chain and product rules respectively
*Simple cases of integration using partial fractions
*Analytical solution of simple first order differential equations with separable variables
*Numerical integration of functions
</onlyinclude>
== Preparation ==
== Supporting activities ==
== Consolidation ==
== Homework ==
== Key questions ==
== Assessment ==
== Notes ==

@@ Line 36: / Line 36: @@
 * Can you see that the chain rule has (nearly) happened?
 ** Like <math>x\sin{x^2}</math>?
-*** Try <math>\sin{x^2}</math>, differentiate, adjust.
+*** Try <math>\cos{x^2}</math>, differentiate, adjust.
 * Is it 'by parts'?
 ** Is it a product of 'something that will disappear if differentiated' and 'something you can integrate'? Like <math>xe^x</math>?

@@ Line 38: / Line 38: @@
 *** Try <math>\sin{x^2}</math>, differentiate, adjust.
 * Is it 'by parts'?
-** Is it a product of 'something that will disappear if differentiated' and 'something you can integrate'? Like <math>x\e^x</math>?
+** Is it a product of 'something that will disappear if differentiated' and 'something you can integrate'? Like <math>xe^x</math>?
 *** Use the 'integration by parts' formula in the formula book.
 * Does the question say 'substitution'?
 ** Do it by substitution. Don't forget to change the <math>dx</math> and the limits.

@@ Line 19: / Line 19: @@
 * Is it standard?
 ** Polynomial like <math>x^3+{\dfrac{x}{5}}^{-\frac{3}{2}}</math>?
-** Basic trig. functions like <math>\sin{x}</math>, <math>\cos{x}</math>?
+** Basic trig. functions like <math>\sin{x}</math> or <math>\cos{x}</math>?
-** Things on the formula sheet like <math>\tan{x}</math>, <math>\sec{x}</math>?
+** Things on the formula sheet like <math>\tan{x}</math> or <math>\sec{x}</math>?
 *** Then just do it.
 * Is it standard with a linear 'inside' function?
-** Like <math>\sin{(3x+2)}</math>, <math>(5x+1)^{-2}</math>?
+** Like <math>\sin{(3x+2)}</math> or <math>(5x+1)^{-2}</math>?
 *** Do it as if it was just <math>x</math>, differentiate, adjust.
 * Could you use a trig. identity?

@@ Line 23: / Line 23: @@
 *** Then just do it.
 * Is it standard with a linear 'inside' function?
-** Like <math>\sin{(3x+2)}</math>, <math>(\dfrac{(5x+1)}{2})^{-2}</math>?
+** Like <math>\sin{(3x+2)}</math>, <math>(5x+1)^{-2}</math>?
 *** Do it as if it was just <math>x</math>, differentiate, adjust.
 * Could you use a trig. identity?

@@ Line 18: / Line 18: @@
 === Integration 'flowchart' ===
 * Is it standard?
-** Polynomial like <math>x^3+\frac{x^{-\frac{3}{2}}}{5}</math>?
+** Polynomial like <math>x^3+{\dfrac{x}{5}}^{-\frac{3}{2}}</math>?
 ** Basic trig. functions like <math>\sin{x}</math>, <math>\cos{x}</math>?
 ** Things on the formula sheet like <math>\tan{x}</math>, <math>\sec{x}</math>?
-Then just do it.
+*** Then just do it.
 * Is it standard with a linear 'inside' function?
-** Like <math>\sin{3x+2}</math>, <math>(\frac{5x+1}{2})^{-2}</math>?
+** Like <math>\sin{(3x+2)}</math>, <math>(\dfrac{(5x+1)}{2})^{-2}</math>?
-Do it as if it was just <math>x</math>, differentiate, adjust.
+*** Do it as if it was just <math>x</math>, differentiate, adjust.
 * Could you use a trig. identity?
 ** Like <math>\cos^2{x}</math>?
 * Could you use partial fractions?
 ** Like <math>\dfrac{x+1}{(x-1)(2x+1)}</math>?
 * Is the numerator (nearly) the derivative of the denominator?
 ** Like <math>\dfrac{x}{x^2+1}</math>?
-Try <math>\ln{|x^2+1|}</math>, differentiate, adjust.
+*** Try <math>\ln{|x^2+1|}</math>, differentiate, adjust.
 * Can you see that the chain rule has (nearly) happened?
 ** Like <math>x\sin{x^2}</math>?
-Try <math>\sin{x^2}</math>, differentiate, adjust.
+*** Try <math>\sin{x^2}</math>, differentiate, adjust.
 * Is it 'by parts'?
 ** Is it a product of 'something that will disappear if differentiated' and 'something you can integrate'? Like <math>x\e^x</math>?
-Use the 'integration by parts' formula in the formula book.
+*** Use the 'integration by parts' formula in the formula book.
 * Does the question say 'substitution'?
 ** Do it by substitution. Don't forget to change the <math>dx</math> and the limits.

@@ Line 13: / Line 13: @@
 == Consolidation ==
 == Homework ==
 == Key questions ==
 == Assessment ==

← Older revision		Revision as of 12:55, 8 January 2014
Line 16:		Line 16:
	== Assessment ==		== Assessment ==
	== Notes ==		== Notes ==
		+	=== Integration 'flowchart' ===
		+	* Is it standard?
		+	** Polynomial like <math>x^3+\frac{x^{-\frac{3}{2}}}{5}</math>?
		+	** Basic trig. functions like <math>\sin{x}</math>, <math>\cos{x}</math>?
		+	** Things on the formula sheet like <math>\tan{x}</math>, <math>\sec{x}</math>?
		+	Then just do it.
		+	* Is it standard with a linear 'inside' function?
		+	** Like <math>\sin{3x+2}</math>, <math>(\frac{5x+1}{2})^{-2}</math>?
		+	Do it as if it was just <math>x</math>, differentiate, adjust.
		+	* Could you use a trig. identity?
		+	** Like <math>\cos^2{x}</math>?
		+	* Could you use partial fractions?
		+	** Like <math>\dfrac{x+1}{(x-1)(2x+1)}</math>?
		+	* Is the numerator (nearly) the derivative of the denominator?
		+	** Like <math>\dfrac{x}{x^2+1}</math>?
		+	Try <math>\ln{\|x^2+1\|}</math>, differentiate, adjust.
		+	* Can you see that the chain rule has (nearly) happened?
		+	** Like <math>x\sin{x^2}</math>?
		+	Try <math>\sin{x^2}</math>, differentiate, adjust.
		+	* Is it 'by parts'?
		+	** Is it a product of 'something that will disappear if differentiated' and 'something you can integrate'? Like <math>x\e^x</math>?
		+	Use the 'integration by parts' formula in the formula book.
		+	* Does the question say 'substitution'?
		+	** Do it by substitution. Don't forget to change the <math>dx</math> and the limits.

@@ Line 2: / Line 2: @@
 == Objectives ==
 <onlyinclude>
-*Integration of <math>e^x</math>, <math>\frac{1}{x}</math>, <math>\sin{x}<\math>, <math>\cos{x}<\math>
+*Integration of <math>e^x</math>, <math>\frac{1}{x}</math>, <math>\sin{x}</math>, <math>\cos{x}</math>
 *Evaluation of volume of revolution
 *Simple cases of integration by substitution and integration by parts. These methods as the reverse processes of the chain and product rules respectively

C4 Integration - Revision history

IDI: /* Homework */

IDI: /* Integration 'flowchart' */

IDI: /* Integration 'flowchart' */

IDI: /* Integration 'flowchart' */

IDI: /* Integration 'flowchart' */

IDI: /* Integration 'flowchart' */

IDI: /* Notes */

IDI: /* Objectives */

Ian: Created page with "Part of C4 == Objectives == *Integration of e^x, \frac{1}{x}, \sin{x}<\math>, \cos{x}<\math> *Evaluation of volume of r..."

Ian: Created page with "Part of C4 == Objectives == Integration of $e^x$ , $\frac{1}{x}$ , $\sin{x}<\math>, \cos{x}<\math> Evaluation of volume of r..."$