Category:Leibniz's Integral Rule

This category contains pages concerning Leibniz's Integral Rule:

Let $\map f {x, t}$, $\map a t$, $\map b t$ be continuously differentiable real functions on some region $R$ of the $\tuple {x, t}$ plane.

Then for all $\tuple {x, t} \in R$:

$\ds \frac \d {\d t} \int_{\map a t}^{\map b t} \map f {x, t} \rd x = \map f {\map b t, t} \frac {\d b} {\d t} - \map f {\map a t, t} \frac {\d a} {\d t} + \int_{\map a t}^{\map b t} \frac \partial {\partial t} \map f {x, t} \rd x$