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Could anyone please explain / derive this formula for me? I encountered it in a probability textbook but can't understand it:

Suppose we have an integral in the following form: $$ R(\alpha) = \int_{a(\alpha)}^{b(\alpha)} r(\alpha , x)dx $$ Then, $$ \frac{dR(\alpha)}{d\alpha} = -r(\alpha , a(\alpha)) \frac{da(\alpha)}{d\alpha} + r(\alpha , b(\alpha)) \frac{db(\alpha)}{\alpha} + \int_{a(\alpha)}^{b(\alpha)} \frac{\partial r(\alpha, x)}{\partial \alpha} dx $$

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This is the Leibniz integral rule.

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  • $\begingroup$ And a very handy tool! $\endgroup$ – JohnD Dec 15 '12 at 20:18

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