Integrating+Higher+Power+Trigonometric+Functions

=**Integrating Higher Power Trigonometric Functions-Ben Edgar**=

**Odd Powers of Sine and Cosine:**
Evaluate the integral: To evaluate this integral, first we have to split up the function into one and one. Than we can use trigonometric properties to change into. From there, it's all about multiplying out the and then distributing the  to each term. Then we can split up all of the terms into separate integrals and integrate them using the power rule. Steps: )

To evaluate something like, the same technique is used, where the function is split up to be one and one.

**Double-Argument Properties for Sine and Cosine:**
and cannot be evaluated with the same technique shown above. Instead, double-argument properties must be used. Properties:

With these properties, integrating and  becomes much easier. Two examples:

ALSO we need to know how to integrate stuff like so... for that, we think about how the derivative of is AND so =

**Integrating even powers of Secant and Cosecant**
We can use the same technique for integrating even powers of sec and cosecant that we used for integrating odd powers of sine and cosine because and && and. So lets try it out. For you do the same thing, but don't forget the negative sign!

[|YouTube - //Integration of Powers// of //Trig Functions//]
Source: Calculus: Concepts and Applications by Paul A. Foerster

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