Trig integration

  • #1
How do you integrate even powers of trig functions, such as

[tex]\int\cos^{2}{\theta} \,d\theta[/tex]
 

Answers and Replies

  • #2
phy
Just an idea: perhaps you could break the integral into cos(theta)*cos(theta) and then integrate by parts from there :smile:
 
  • #3
tandoorichciken, you must use an identity

[tex]

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

[/tex]

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

[tex]
cos^4 \theta = (cos^2)^2 = (\frac{1 + cos 2\theta}{2})^2
[/tex]

For the sine function, use the identity

[tex]

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

[/tex]

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

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