- #1

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(Assume that all are differentiable enough times):

Calculate:

[tex]

\frac{\mathrm{d} }{\mathrm{d} x}\int_{g(x)}^{h(x)} f(x,t) dt

[/tex]

- Thread starter mathmadx
- Start date

- #1

- 17

- 0

(Assume that all are differentiable enough times):

Calculate:

[tex]

\frac{\mathrm{d} }{\mathrm{d} x}\int_{g(x)}^{h(x)} f(x,t) dt

[/tex]

- #2

HallsofIvy

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Homework Helper

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Leibniz's rule, which generalizes the fundamental theorem of Calculus:

(Assume that all are differentiable enough times):

Calculate:

[tex]

\frac{\mathrm{d} }{\mathrm{d} x}\int_{g(x)}^{h(x)} f(x,t) dt

[/tex]

[tex]\frac{d}{dx} \int_{g(x)}^{h(x)} f(x,t)dt= \frac{dh}{dx}f(x, h(x))- \frac{dg}{dx}f(x,g(x))+ \int_{g(x)}^{h(x)} \frac{\partial f(x,t)}{\partial x} dt[/tex]

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