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Math Help - Integral of a product

  1. #1
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    Integral of a product

    Hi im developing a method which uses are dirichlet distribution

    I am however using a frequency range and so have to include an integral. I am however stuck trying to evaluate this integral. What confuses me is the product

    \int \prod T^O dT


    if anyone can help
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  2. #2
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    i forgot to add the integral is taken from u to v

    and the product from 1 to k
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by chogo View Post
    Hi im developing a method which uses are dirichlet distribution

    I am however using a frequency range and so have to include an integral. I am however stuck trying to evaluate this integral. What confuses me is the product

    \int \prod T^O dT


    if anyone can help
    Do you mean:

    \int_u^v \prod_{i=1}^k T^{O_i}\ dT\ \ \ ?

    RonL
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  4. #4
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    yes sorry i was given the wrong equation, the one you have written is correct

    how do i evaluate that integral? is it anything tricky or is it just the trivial solution i think it is?
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  5. #5
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    so does anyone know how to solve this integral? or should i just implement simpsons rule for an aproximate solution?
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by chogo View Post
    so does anyone know how to solve this integral? or should i just implement simpsons rule for an aproximate solution?
    Assuming \sum_{i=1}^kO_i \ne -1

    \int_u^v \prod_{i=1}^k T^{O_i}\ dT=\int_u^v T^ {\sum_{i=1}^kO_i}\ dT=\left. \frac{1}{(\sum_{i=1}^kO_i) +1}T^ {(\sum_{i=1}^kO_i)+1}\right|_{T=u}^v

    RonL
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