Hello

I'm trying to find the indefinite integral of $\displaystyle x^{550} * (1-x)^{450}$.

How do I do this? I tried by parts but it seems to be about 450 iterations long! :) Any good substitution tricks or am I missing something?

Thanks!

Thomas

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- Oct 31st 2008, 05:03 AMTornamHow to integrate this function?
Hello

I'm trying to find the indefinite integral of $\displaystyle x^{550} * (1-x)^{450}$.

How do I do this? I tried by parts but it seems to be about 450 iterations long! :) Any good substitution tricks or am I missing something?

Thanks!

Thomas - Oct 31st 2008, 05:30 AMHallsofIvy
No substitutions. You could try using the binomial theorem to say that $\displaystyle (1-x)^{450}= \sum_{i=0}^{450}C(450 i) (-1)^{450-i}x^i$, where C(n, i) is the binomial coefficient, which is the same as $\displaystyle \sum_{i=0}^{450} C(450,i) (-1)^ix^i$ since 450-i is odd if and only if i is.

Then $\displaystyle x^{550}(1- x)^{450}= \sum_{i=0}^{450} C(450,i) (-1)^i x^{i+ 550}$ and integrate term by term. - Oct 31st 2008, 06:18 AMTornam
Ah yes. What do you mean term by term though? As in integrate every term in the sum?

Thanks for your help!! - Oct 31st 2008, 06:44 PMMathstud28