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Math Help - integrals

  1. #1
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    integrals

    what if x appears inside the integral?
    find f'(x) for f(x) = integral from a to b of g(x,t) dt

    and then

    use this result to evaluate I= integral from 0 to 1 of (t^2)*(e^(-t)) dt
    and they give you a hint which makes no sense to me

    Hint: Compute integral from 0 to 1 of e^(-st) dt
    where s is a parameter
    How is I related to this integral?
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  2. #2
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    Quote Originally Posted by razorfever View Post
    what if x appears inside the integral?
    find f'(x) for f(x) = integral from a to b of g(x,t) dt

    and then

    use this result to evaluate I= integral from 0 to 1 of (t^2)*(e^(-t)) dt
    and they give you a hint which makes no sense to me

    Hint: Compute integral from 0 to 1 of e^(-st) dt
    where s is a parameter
    How is I related to this integral?
    I think this is what there getting at.

    If (1)\;\;\;g(s) = \int_0^1 e^{-st}\,dt then

    g''(s) = \int_0^1 t^2 e^{-st}\,dt

    and
    g''(1) = \int_0^1 t^2 e^{-t}\,dt your integral. Now from (1), integrate to find g(s) differentiate twice and evaluate at s = 1.
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