Re: Integral of even functions

On May 27, 4:41 pm, esej...@xxxxxxxxx wrote:
Hi there!
I came across an interesting thing. Integration of some even functions
from minus infinity to plus infinity is equal to zero. I have observed
similar thing for some Hermitian functions. Is this fact well known in
mathematics? If yes, what are the cases when this is true?
Thanks!

Did you perhaps mean to say that integration
of some _odd_ functions from -oo to +oo gives
zero (when the improper integral converges)?

It would be something of a special case for
such an integral of an even function to give
zero.

Consider "bell curve" y = e^(-x^2).
It's obviously an even function, and the
integral over (-oo,+oo) can be peformed by
a well-known trick using polar coordinates:

http://planetmath.org/encyclopedia/AreaUnderTheBellCurve.html

to give area sqrt(pi).

regards, chip

.

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