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Thread: Derivative of an integral

  1. September 10th 2011, 07:12 AM #1
    flybynight
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    Derivative of an integral

    Hey guys,
    I am looking at this problem, and I don't have any idea how to do it: \frac{d}{dx}\int_x^3e^{{-t}^2}dt

    Any help would be greatly appreciated.
    Thanks,
    Peter
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  2. September 10th 2011, 07:25 AM #2
    Plato
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    Re: Derivative of an integral

    Quote Originally Posted by flybynight View Post
    Hey guys,
    I am looking at this problem, and I don't have any idea how to do it: \frac{d}{dx}\int_x^3e^{{-t}^2}dt
    Suppose that each of g~\&~h is s differentiable function then
    \frac{d}{{dx}}\int_{h(x)}^{g(x)} {f(t)dt} = g'(x)f(g(x)) - h'(x)f(h(x)).
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