Integrals of symmetric functions.
Sometimes, a function’s symmetry can make it easier to evaluate integrals of the function. If f(x) is an odd function, then for any . If is an even function, then for any , where it is usually easier to evaluate the antiderivative at 0 than at .
Even and odd functions arise in many situations. Symmetry allows integrals involving these functions to be evaluated more easily.
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