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Math Help - Fundamentals of Calc

  1. #1
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    Fundamentals of Calc

    Let G(x) be the integral of f(t)=sin(t) over the interval [0, x], x>0. Which of the following is G'(x), the derivative of G(x) with respect to x?

    cos (x)
    cos (t)
    sin (x)
    sin (t)
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by Billy Maize View Post
    Let G(x) be the integral of f(t)=sin(t) over the interval [0, x], x>0. Which of the following is G'(x), the derivative of G(x) with respect to x?

    cos (x)
    cos (t)
    sin (x)
    sin (t)
    sin(x)
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  3. #3
    Member eXist's Avatar
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    Amer is correct. In general:

    \frac{d}{dx} \left[ \int_a^u f(t) dt\right] = f(u) \cdot \frac{du}{dx}<br />
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