I found a particular integral in my stat book.(adsbygoogle = window.adsbygoogle || []).push({});

[itex] \frac{d}{ d\theta}\int^{b(\theta)}_{a(\theta)}f(\theta,t)dt =

\int^{b(\theta)}_{a( \theta)}\frac{ \partial}{ \partial \theta}f( \theta ,t)dt +

f( \theta, b( \theta)) \frac {\partial b(\theta)}{ \partial \theta} -

f(\theta, a(\theta))\frac{ \partial a(\theta)}{\partial \theta} [/itex]

Why is this the case? Why is it not...

[itex] \int^{b(\theta)}_{a(\theta)}f(\theta,t)dt =

\int^{b(\theta)}_{a( \theta)}\frac{ \partial}{ \partial \theta}f( \theta ,t)dt +

\frac{d}{ d\theta} [F( \theta, b( \theta)) - F(\theta, a(\theta))]

[/itex]

EDITED: Fixing LaTeX, as per usual. Sorry Folks.

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# Leibnitz Rule For an Integral.

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