Trig integration

[tandoorichicken]

How do you integrate even powers of trig functions, such as

\int\cos^{2}{\theta} \,d\theta

[phy]

Just an idea: perhaps you could break the integral into cos(theta)*cos(theta) and then integrate by parts from there :smile:

[relinquished™]

tandoorichciken, you must use an identity



cos^2 \theta = \frac{1 + cos 2\theta}{2}



When the cosine function is raised to an even integer, say for example 4,


cos^4 \theta = (cos^2)^2 = (\frac{1 + cos 2\theta}{2})^2


For the sine function, use the identity



sin^2 \theta = \frac{1 - cos 2\theta}{2}



A word of Caution. When doing this method do not forget to double your angle ^_^