| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Another quickie.
Proposed by Murray S. Klamkin, University of Alberta, Edmonton,
Alberta, Canada.
Determine int((1-x^m)^n,x=0..1) / int((1-x^m)^(n-1),x=0..1), m, n > 0,
without using beta function integrals.
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1946.1 | integration by parts | HERON::BUCHANAN | Et tout sera bien et | Mon Mar 06 1995 10:29 | 14 |
> Determine int((1-x^m)^n,x=0..1) / int((1-x^m)^(n-1),x=0..1), m, n > 0, > without using beta function integrals. Fortunately, I don't know what a beta function integral is, so I have no difficulty in tackling this problem :-) Let F(m,n) = int((1-x^m)^n,x=0..1). Integrating this by parts, we get that: F(m,n) = (nm/(nm+1))*F(m,n-1) So the answer we're looking for is nm/(nm+1). Andrew. | |||||