Re: definite and indefinite Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg50445] Re: definite and indefinite Integrate
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Sat, 4 Sep 2004 01:43:21 -0400 (EDT)
- References: <ch97sp$ffg$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Jun Yan <jyan at stat.wisc.edu> wrote:
> This is a question from a beginner:
>
> ff[z_] = 1/z + z^3
> Integrate[ff[z], {z, y, y0}]
> intff[z_] = Integrate[ff[z], z]
> intff[y] - intff[y0]
>
> I expected to get same results from line 2 and line 4. However, the
> output from line 2 is very complicated, with an If which has Im(y) and
> Im(y0) involved. The result I want is that from line 4. How can I modify
> line 2 so that it produces the same output as from line 4?
Change the order of integration and add appropriate assumptions:
Integrate[ff[z], {z, y0, y}, Assumptions -> 0 < y0 < y]
(1/4)*(y^4 - y0^4) + Log[y/y0]
which I hope you'll agree is even a bit nicer than the output from your
line 4.
David Cantrell