Lec 3 - Trigonometric Integrals

- Substitution
- Integration by Parts

Recall: Techniques of Integration

(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.

This is a polynomial. Expand then integrate.

Similarly, we can evaluate the integral

Created by Tim Pei with Microsoft OneNote 2010

One place for all your notes and information