The integral is from [0,1] and the equation is x*(1-x)^n for n being any positive integer.

just a side note, I tried subbing u=1-x, but I still end up with 1-u*u^n and don't really know what to do with that

2. Originally Posted by cloverz7
The integral is from [0,1] and the equation is x*(1-x)^n for n being any positive integer.

just a side note, I tried subbing u=1-x, but I still end up with 1-u*u^n and don't really know what to do with that
Your side note is a good idea: it remains to expand $\int_0^1 (1-u)u^n du=\int_0^1 u^n du - \int_0^1 u^{n+1} du$ and compute the two rather simple integrals.

3. do you have to seperate them like that? it just kind of makes computation a little more aggrivating using two fundamental theorems.

4. Originally Posted by cloverz7
do you have to seperate them like that? it just kind of makes computation a little more aggravating using two fundamental theorems.
Well, this is already very simple as such (both integrals are really easy)...

If you really don't want to split the integral, you can expand inside the integral and find an antiderivative of $x^n-x^{n+1}$, this is just the same...