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Thread: Deriv of an Integral

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    Deriv of an Integral

    Let F(x) = integral from x^2 to x^3 of sin (t^2) dt. What is F'(x)? (This problem cannot be addressed by trying to work the integral.)
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    Re: Deriv of an Integral

    Quote Originally Posted by Headinthesand View Post
    Let F(x) = integral from x^2 to x^3 of sin (t^2) dt. What is F'(x)? (This problem cannot be addressed by trying to work the integral.)
    Suppose $h~\&~g$ is a differentiable function. If $\large\displaystyle F(x) = \int_{h(x)}^{g(x)} {\Phi (t)dt}$ then $\large F'(x) = g'(x) \cdot \Phi \circ g(x) - h'(x) \cdot \Phi \circ h(x)$.
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