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Math Help - How to integrate this function?

  1. #1
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    How to integrate this function?

    Hello

    I'm trying to find the indefinite integral of 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
    Last edited by Tornam; October 31st 2008 at 06:18 AM.
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  2. #2
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    Quote Originally Posted by Tornam View Post
    Hello

    I'm trying to find the indefinite integral of 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
    No substitutions. You could try using the binomial theorem to say that (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 \sum_{i=0}^{450} C(450,i) (-1)^ix^i since 450-i is odd if and only if i is.

    Then x^{550}(1- x)^{450}= \sum_{i=0}^{450} C(450,i) (-1)^i x^{i+ 550} and integrate term by term.
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  3. #3
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    Ah yes. What do you mean term by term though? As in integrate every term in the sum?

    Thanks for your help!!
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Tornam View Post
    Ah yes. What do you mean term by term though? As in integrate every term in the sum?

    Thanks for your help!!
    \int{\sum_{n=0}^{450}}{_{450}}C_n(-1)^nx^{n+450}dx

    =\sum_{n=0}^{450}\int{_{450}C_n}(-1)^nx^{n+550}dx

    =\sum_{n=0}^{450})\frac{_{450}C_n(-1)^nx^{n+551}}{551}+C
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