|
|
In article <1162328863.915031.86810@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
dale6998 <dale.goodman@xxxxxxxxxxxxxx> wrote:
>Suppose that f(x) is a continuous function defined for all x. Prove
>that if f(x) is even then it has exactly one odd antiderivative.
>
>Good Luck
Thanks; but I don't think I need it...
HINT the First: If g(x) is an odd function, what is g(0)?
HINT the Second: If g(x) and h(x) are two antiderivatives of f(x),
then g(x) = h(x) + C, where C is a constant. So... what is the largest
number of odd antiderivatives that a function may have?
HINT the Third: The Fundamental Theorem of Calculus gives you a
particular antiderivative. Can you use that to try to find an odd
antiderivative?
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================
Arturo Magidin
magidin-at-member-ams-org
|
|