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April 12th, 2015, 06:02 PM  #1 
Newbie Joined: Apr 2015 From: Milwaukee Posts: 1 Thanks: 0  Derivative of integral with variables as limits of integration? Fundamental theorem o
I need to find the derivative of the integral of a function as shown in the picture. But the limits of integration are variables and I don't know how to go about solving this. Please help me! Any guidance is greatly appreciated. Thank you in advance. 
April 12th, 2015, 06:39 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677 
let $u$ and $v$ be functions of $x$ ... $\displaystyle \frac{d}{dx} \int_u^v f(j) \, dj = f(v) \cdot v'  f(u) \cdot u'$ 

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derivative, fundamental, integral, integration, limits, theorem, variables 
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