Solution 2.1:3b

From Förberedande kurs i matematik 2

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m (Lösning 2.1:3b moved to Solution 2.1:3b: Robot: moved page)
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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,
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<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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<math>\int{\sin 2x}\,dx=-\frac{\cos 2x}{2}+C</math>
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where
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<math>C</math>
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is an arbitrary constant.

Revision as of 13:41, 17 October 2008

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.

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