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Citation bot (talk | contribs) Add: author-link1, authors 1-1. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Dominic3203 | Linked from User:Jim.belk/Most_viewed_math_articles_(2010) | #UCB_webform_linked 302/998 |
integral -inf to inf of odd function = 0 holds for Cauchy principal value |
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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''
*:<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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