This integral make me confused: show int[x^m (1-x)^n]dx =...

[Guest]

show that
\(\displaystyle \L\int_0^{1} x^m(1-x)^ndx=\frac {n}{m+1}\int_0^{1} x^{m+1}(1-x)^{n-1}dx\)
hence show that
\(\displaystyle \L\int_0^{1} x^m(1-x)^ndx=\frac{m!n!}{(m+n+1)!}\)
thanx :?

 

[galactus]

Try this link. See page 3.

http://www.math.umn.edu/~keel/tfall2004 ... utions.pdf