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Even and odd functions: Difference between revisions

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→Even–odd decomposition: ending section with sentence linking to sine and cosine transforms.
Weaken requirement for integration interval be finite.
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* The [[derivative]] of an even function is odd.
* The derivative of an odd function is even.
* The [[integral]] of an odd function from −''A'' to +''A'' is zero (where ''A'' iscan be finite or infinite, and the function has no vertical asymptotes between −''A'' and ''A''). For an odd function that is integrable over a symmetric interval, e.g. <math>[-A,A]</math>, the result of the integral over that interval is zero; that is<ref>{{cite web|url=http://mathworld.wolfram.com/OddFunction.html|title=Odd Function|first=Weisstein, Eric|last=W.|website=mathworld.wolfram.com}}</ref>
*:<math>\int_{-A}^{A} f(x)\,dx = 0</math>.
* The integral of an even function from −''A'' to +''A'' is twice the integral from 0 to +''A'' (where ''A'' is finite, and the function has no vertical asymptotes between −''A'' and ''A''. This also holds true when ''A'' is infinite, but only if the integral converges); that is
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