Integral/Powers of sine/Recursion/Example

From Wikiversity
Jump to navigation Jump to search

A primitive function for the sine function is . In order to find a primitive function for , we use integration by parts to get a recursive relation to a power with a smaller exponent. To make this more precise, we work over an interval, the primitive function shall start at and have the value there. For , with integration by parts, we get

Multiplication with and rearranging yields

In particular, for , we have