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Math Help - derivative of an integral?

  1. #1
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    derivative of an integral?

    \int_{\sqrt{x}}^ x \frac{cos z}{z} dz

    I have no idea what to do.
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  2. #2
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    You could try integration by parts in the form

    \int_{\sqrt{x}}^ x z^{-1}\cos( z) ~dz

    or use a series approximation for \cos(z)
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  3. #3
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    Quote Originally Posted by yoman360 View Post
    \int_{\sqrt{x}}^ x \frac{cos z}{z} dz

    I have no idea what to do.
    the Fundamental Theorem of Calculus ...

    u and v are both functions of x

    \frac{d}{dx} \left[ \int_v^u f(z) \, dz \right] = f(u) \cdot \frac{du}{dx} - f(v) \cdot \frac{dv}{dx}
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  4. #4
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    Quote Originally Posted by skeeter View Post
    the Fundamental Theorem of Calculus ...

    u and v are both functions of x

    \frac{d}{dx} \left[ \int_v^u f(z) \, dz \right] = f(u) \cdot \frac{du}{dx} - f(v) \cdot \frac{dv}{dx}
    I never seen a problem like this before and now thanks to you i know how to solve it when i see it again
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