Content deleted Content added
→Teddy theorem: new section |
→Integral of an odd function: fixing ref format |
||
Line 51:
==Integral of an odd function==
For an odd function <math>f(x)</math> the integral <math>\int_{-A}^{A} f(x) dx = 0</math> even when <math>A = \infty</math>. The statement that <math>A</math> must be finite is incorrect. My contribution to this paragraph has this citation, the original content appears to have no citation for to support its incorrect assertion.<ref>http://mathworld.wolfram.com/OddFunction.html</ref>
:{{ping|MathInclined}} This is not true. <math>\int_{-\infty}^{+\infty} x dx</math> does not even exist. If one wants to make sense of that, one must generally resort to [[Cauchy principal value]]s. This is not contradicted by the link you gave, which deals with bounded intervals only. The subtle point is the meaning of integrability over the whole real line.--[[User:Jasper Deng|Jasper Deng]] [[User talk:Jasper Deng|(talk)]] 07:45, 11 December 2017 (UTC)
{{reftalk}}
== Teddy theorem ==
| |||