Lec 3 - Trigonometric Integrals

Recall: Techniques of Integration

1. Substitution
2. Integration by Parts

 

(7.2)

 

Example

Find a reduction formula:



 

Solution:



 

Use integration by parts



 

 



 







 







 

 

Example





 





 

Example



(could apply reduction formula or half angle formula)

 





 

(use double angle formula again)

 





 

 

Now we consider odd powers.

 

Example





 

(use trig identity)

 



 





 







 

 Generally,









 



You expand the polynomial and then integrate each term.

 

 More generally, consider



There are 3 cases to consider.

 

1. 







This is a polynomial. Expand then integrate.

 

2. 







 

3. 







 

 

 Similarly, we can evaluate the integral