Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 William Elliot Posts: 1,948 Registered: 5/30/08
Re: Indefinite integral puzzle
Posted: Dec 30, 2010 1:24 AM

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

Date Subject Author
12/29/10 Craig Feinstein
12/29/10 Frederick Williams
12/30/10 William Elliot
12/30/10 Pfsszxt@aol.com
12/30/10 Craig Feinstein
12/31/10 William Elliot
12/31/10 Craig Feinstein
12/31/10 Phil H