Solids - Revision history

DavidB4-bot: clean up & uniformity

2016-07-13T19:29:33Z

clean up & uniformity

2012-01-12T06:57:46Z

Reverted edits by Billtannan (talk) to last version by Aschlafly

2012-01-12T06:45:58Z

Reverted edits by Billtannan (talk) to last revision by NathanG

2012-01-12T06:26:15Z

clean up

2008-03-15T00:18:08Z

bold

2007-12-16T21:21:44Z

corrected

2007-12-16T21:20:55Z

corrected

2007-12-16T21:17:52Z

corrected

2007-12-16T19:52:53Z

2007-12-16T19:52:30Z

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 In [[calculus]], '''solids''' are formed by rotating a curve around an axis and integrating to find the volume.  Typically the [[integration]] is of slices cut vertically to the axis of the rotation that formed the solid.  Those slices are then integrated from one end of the solid to the other.
@@ Line 56: / Line 54: @@
 and the solution to the overall integral is easy to obtain.
-[[category:mathematics]]
+[[Category:Mathematics]]
-[[category:calculus]]
+[[Category:Calculus]]

← Older revision		Revision as of 06:57, January 12, 2012
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	In [[calculus]], '''solids''' are formed by rotating a curve around an axis and integrating to find the volume. Typically the [[integration]] is of slices cut vertically to the axis of the rotation that formed the solid. Those slices are then integrated from one end of the solid to the other.		In [[calculus]], '''solids''' are formed by rotating a curve around an axis and integrating to find the volume. Typically the [[integration]] is of slices cut vertically to the axis of the rotation that formed the solid. Those slices are then integrated from one end of the solid to the other.

← Older revision		Revision as of 06:45, January 12, 2012
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−	~~<nowiki>~~
−
	In [[calculus]], '''solids''' are formed by rotating a curve around an axis and integrating to find the volume. Typically the [[integration]] is of slices cut vertically to the axis of the rotation that formed the solid. Those slices are then integrated from one end of the solid to the other.		In [[calculus]], '''solids''' are formed by rotating a curve around an axis and integrating to find the volume. Typically the [[integration]] is of slices cut vertically to the axis of the rotation that formed the solid. Those slices are then integrated from one end of the solid to the other.

← Older revision		Revision as of 06:26, January 12, 2012
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		+	<nowiki>
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	In [[calculus]], '''solids''' are formed by rotating a curve around an axis and integrating to find the volume. Typically the [[integration]] is of slices cut vertically to the axis of the rotation that formed the solid. Those slices are then integrated from one end of the solid to the other.		In [[calculus]], '''solids''' are formed by rotating a curve around an axis and integrating to find the volume. Typically the [[integration]] is of slices cut vertically to the axis of the rotation that formed the solid. Those slices are then integrated from one end of the solid to the other.

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-In [[calculus]], solids are formed by rotating a curve around an axis and integrating to find the volume.  Typically the [[integration]] is of slices cut vertically to the axis of the rotation that formed the solid.  Those slices are then integrated from one end of the solid to the other.
+In [[calculus]], '''solids''' are formed by rotating a curve around an axis and integrating to find the volume.  Typically the [[integration]] is of slices cut vertically to the axis of the rotation that formed the solid.  Those slices are then integrated from one end of the solid to the other.
 == Example ==
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 Recall that:
-:<big><big><math>\int\sec^2{x}\,dx = \tan{x}</math></big></big>
+:<big><math>\int\sec^2{x}\,dx = \tan{x}</math></big>
 and the solution to the overall integral is easy to obtain.
 [[category:mathematics]]
 [[category:calculus]]

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 :<math>\int_0^\frac{\pi}{4}(\sec{x}\,\tan{x})^2\,dx</math>
-:<math> = \int_0^\frac{\pi}{4}\sin{x}\,(\frac{\sin{x}}{\cos^3{x}})\,dx</math>
+:<math> = \int_0^\frac{\pi}{4}\sin{x}\,(\frac{\sin{x}}{\cos^4{x}})\,dx</math>
-:<math> = \frac{\sin{x}}{2\cos^2{x}} - \int_0^\frac{\pi}{4}\frac{\sec{x}}{2},\,dx</math>
+:<math> = \frac{\sin{x}}{3\cos^3{x}} - \int_0^\frac{\pi}{4}\frac{\sec^2{x}}{3},\,dx</math>
 Recall that: