MAT136H1 Lecture Notes - List Of Trigonometric Identities
7.2 Integration Techniques
Question #2 (Medium): Evaluating the Integral of Sine & Cosine With Even Power
When and or are raised to even power, half-angle identities are helpful in reducing the even
power by half every time it is applied. Then the reduced power, in conjunction with trigonometric
identities, the integral can be simplified and evaluated.
Evaluate the integral.
Since both and are raised to even power, no single term can be isolated. By applying half-
angle identities, even power is reduced by half every time it is applied. So here:
Then the three components in the integral can be evaluated separately.
. Let , then
Substituting into the integral,
Put all three pieces together:
Therefore, the integral is evaluated as: