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:
We have:
.
Therefore:
.
Check this result either by differentiation, or by using standard trigonometric identities.
We have:
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Noah Dana-Picard 2007-12-28