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Thread: Derivative of a Integral

  1. #1
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    Derivative of a Integral

    If f(x) = $\displaystyle \int_1^x \sqrt{t^2+3}dt$ , 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$\displaystyle \sqrt(19)$ but I got $\displaystyle \sqrt(7)$.
    Last edited by IsaHanswille; Mar 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) = $\displaystyle \int_1^x \sqrt{t^2+3}dt$ , 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$\displaystyle \sqrt(19)$ but I got $\displaystyle \sqrt(7)$.
    FTC ...

    for a constant $\displaystyle a$ and $\displaystyle u$ a function of $\displaystyle x$ ...

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