Last updated Unknown

Status: Tags: Links: Integral Calculus Notes

Sin and Cosine Power Integration

Odd Powers

Resource

Steps

1. Factor out a term from the odd power using unit circle identity
2. Do the appropriate sinx or cosx u substitution

Even Powers

• Used when integrand contains only even powers of sin, cos, or both

Steps

1. Separate even powers into exponents of 2
2. Use identities to substitute out the even trigs
3. Might have to substitue the interior of a trig function to apply one of the subsitutions below
4. Antiderive

Isolating Cosine

$$cos(2x) = 2cos^2x - 1$$

can be converted into

$$cos^2x = \frac{1}{2} + \frac{1}{2}cos(2x)$$

Isolating Sine

$$cos(2x) = 1 - 2sin^2x$$

can be converted into

$$sin^2x = \frac{1}{2} - \frac{1}{2}cos(2x)$$

References:

Created:: 2021-06-07 16:42