We call here a trigonometric polynomial a linear combination of terms of the form , where and are non negative integers. To compute the integral of a trigonometric polynomial, we must first of all linearize it. For this purpose, we use the so-called Euler's formulae:
We will not develop the general case, but give some examples:
. Therefore: . Check this result either by differentiation, or by using standard trigonometric identities.
Noah Dana-Picard 2007-12-28