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Math Help - Evaluating an Integral

  1. #1
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    Evaluating an Integral

    Assuming ∫ = the integral from (0-3)

    I am having trouble deciding what to sub in as u in this integration problem:

    ∫ x(sqrt(x+1)) dx

    Thanks.
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  2. #2
    Junior Member Bradyns's Avatar
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    Re: Evaluating an Integral

    Let u = x+1, du = dx

    The integral can then be rewritten as:

    \int_{0}^{3} (u-1)(\sqrt{u})du

    I'm sure you can take it from here.
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  3. #3
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    Re: Evaluating an Integral

    Quote Originally Posted by Walshy View Post
    Assuming ∫ = the integral from (0-3)

    I am having trouble deciding what to sub in as u in this integration problem:

    ∫ x(sqrt(x+1)) dx

    The integral \int_0^3 {x\sqrt {x + 1} dx} becomes \int_1^4 {(u - 1)\sqrt u du} .

    Do you see how?
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    Re: Evaluating an Integral

    Yes, I see. Thanks for the help guys.
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    Re: Evaluating an Integral

    Quote Originally Posted by Bradyns View Post
    Let u = x+1, du = dx

    The integral can then be rewritten as:

    \color{red}\int_{0}^{3} (u-1)(\sqrt{u})du
    The limits of integration are not correct.
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  6. #6
    Junior Member Bradyns's Avatar
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    Re: Evaluating an Integral

    Given this, I should clarify that my bounds were regards to X, so when you integrate, you should back substitute U so you are in respect to X before evaluation of the bounds.

    You can change the bounds so that they are with respect to U and integrate.

    Or, you can leave the bounds with regard to X, integrate with respect to U and then back substitute so that you end up with the original function (f(x), not not f'(x)) with respect to X.

    Same result.
    Last edited by Bradyns; May 2nd 2013 at 08:59 PM.
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