Intigrating this seemingly simple expression

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April 3rd 2008, 05:37 PM
jagged

Intigrating this seemingly simple expression

I know that the antiderivative is cos^2(x) is (x+cos(x)sin(x))/2, but how the heck can you derive it?
April 3rd 2008, 05:45 PM
mr fantastic

Quote:

Originally Posted by jagged

I know that the antiderivative is cos^2(x) is (x+cos(x)sin(x))/2, but how the heck can you derive it?

Make the appropriate substitution suggested by the double angle formula:

$\cos (2x) = 2 \cos^2 (x) - 1 \Rightarrow \cos^2 (x) = \frac{1}{2} \, (\cos(2x) + 1)$ .

Then, after integrating, make the substitution $\sin (2x) = 2 \sin x \cos x$ in your answer.
April 3rd 2008, 05:53 PM
jagged

thanks... ive forgotten basic methods of integration since spring break :D

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