Finding the Derivative of an Integral: Explanation Needed

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    Derivative Integral
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Discussion Overview

The discussion revolves around the process of taking the derivative of an integral, specifically in the context of a homework problem involving the equation u(1/r)((d/dr)[(r)(dV/dr)])=P. Participants seek clarification on the steps involved in deriving the correct expression for V from the integral.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant expresses confusion about their attempt at finding V, noting a discrepancy between their result and the expected answer, which includes additional terms.
  • Another participant suggests that the absence of a constant during the initial integration might explain the missing terms in the final expression.
  • A third participant seeks clarification on whether the derivative being discussed is of the integral itself or of a different integral related to the original equation.
  • A later reply points out that this thread appears to be a duplicate of a previous discussion on the same topic.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants presenting different perspectives on the integration process and the handling of constants, but no consensus is reached on the correct approach or solution.

Contextual Notes

Participants have not fully clarified the assumptions regarding the constants involved in the integration process, and there is uncertainty about the specific integral being referenced.

juice34
1. Homework Statement
Can someone help me take the derivative of the integral
u(1/r)((d/dr)[(r)(dV/dr)])=P


2. Homework Equations



3. The Attempt at a Solution
my attempt yields V=(Pr^2)/(2u)+C(1), which is not right. The actual answer is V=(Pr^2)/4u+C(1)ln(r)+C(2). I am having trouble finding out where the 4 and everything else comes from could someone please explain to me what is going on. Thank YOU
 
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When you first integrated, did you include your constant? If not, that might explain why you lacked the extra term upon the second integration.
 
You want to find
[tex]\frac{d}{dx}\int u(1/r)\frac{d\left(r\frac{dV}{dr}\right)}{dr}dr[/tex]?
That, of course, is equal to
[tex]u(1/r)\frac{d\left(r\frac{dV}{dr}\right)}{dr}[/tex]?

Or do you mean the integral of that integral?
 

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