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Topic: Indefinite integral puzzle
Replies: 7   Last Post: Dec 31, 2010 10:50 AM

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William Elliot

Posts: 1,948
Registered: 5/30/08
Re: Indefinite integral puzzle
Posted: Dec 30, 2010 1:24 AM
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On Wed, 29 Dec 2010, Craig Feinstein wrote:

> Let I(f(x))dx be the indefinite integral of a function f(x). Then what
> is:
> I(I(I(I(...)dx)dx)dx)dx ?

For p in R[x],
integral^oo p(x) dx^oo = sum_(j=n,oo) aj.x^j.

integral^oo f(x) dx^oo
= integral^oo f(x) dx^oo + sum_(j=n,oo) aj.x^j.
= integral^oo f(x) dx^oo + integral^oo p(x) dx^oo
= integral^oo (f(x) + p(x)) dx^oo

If f has a Taylor series, then integral^oo f(x) dx^oo
= integral^oo 0 dx^oo = integral^oo p(x) dx^oo

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