From Förberedande kurs i matematik 2

Revision as of 14:37, 16 September 2008 (edit) Tekbot (Talk | contribs) m (Lösning 2.1:3b moved to Solution 2.1:3b: Robot: moved page) ← Previous diff		Current revision (13:13, 21 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	As the integral stands, it is not so easy to see what the primitive functions are, but if we use the formula for double angles,
-	<center> [[Image:2_1_3b.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\int 2\sin x\cos x\,dx = \int \sin 2x\,dx</math>}}
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		+	we obtain a standard integral where we can write down the primitive functions directly,
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		+	{{Displayed math||<math>\int \sin 2x\,dx = -\frac{\cos 2x}{2}+C\,,</math>}}
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		+	where <math>C</math> is an arbitrary constant.

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Current revision

As the integral stands, it is not so easy to see what the primitive functions are, but if we use the formula for double angles,

\displaystyle \int 2\sin x\cos x\,dx = \int \sin 2x\,dx

we obtain a standard integral where we can write down the primitive functions directly,

\displaystyle \int \sin 2x\,dx = -\frac{\cos 2x}{2}+C\,,

where \displaystyle C is an arbitrary constant.