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Math Help - Derivative of a Integral

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    Derivative of a Integral

    If f(x) =  \int_1^x \sqrt{t^2+3}dt , then f`(2)=?
    The integral is from 1 to x^2 but I couldn't figure out how to do that in the integral. Everything else is right.
    So the answer is 4  \sqrt(19) but I got  \sqrt(7).
    Last edited by IsaHanswille; March 11th 2010 at 04:21 PM.
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  2. #2
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    Quote Originally Posted by IsaHanswille View Post
    If f(x) =  \int_1^x \sqrt{t^2+3}dt , then f`(2)=?
    The integral is from 1 to x^2 but I couldn't figure out how to do that in the integral. Everything else is right.
    So the answer is 4  \sqrt(19) but I got  \sqrt(7).
    FTC ...

    for a constant a and u a function of x ...

    if f(x) = \int_a^u g(t) \, dt , then f'(x) = g(u) \cdot \frac{du}{dx}
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