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Derivative of an integral?

  1. Oct 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Can someone help me take the derivative of the integral
    u(1/r)((d/dr)[(r)(dV/dr)])=P


    2. Relevant 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 comes from could someone please explain to me what is going on. Thank YOU
     
  2. jcsd
  3. Oct 8, 2009 #2

    LCKurtz

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    Is u a function of r? If not why write u(1/r) instead of just (u/r)? Are u and P constants? I think I know the answers to those questions but you should pose your question more carefully. Rewriting your equation using ' for d/dr:

    (rV')' = Pr/u

    Integrate:

    rV' = Pr2/(2u) + C

    Divide both sides by r and integrate again.
     
    Last edited: Oct 8, 2009
  4. Oct 8, 2009 #3
    LCKurtz u and P are constant. And im not sure i follow this part, (rV')' = r/u. Is it equal to d/dx(r(dV/dr))
     
    Last edited: Oct 8, 2009
  5. Oct 8, 2009 #4

    LCKurtz

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    I accidently left off the P, which I just edited to correct.

    (rV')' is d/dr (r dV/dr)

    No x in there. Its much neater to write with primes.
     
  6. Oct 9, 2009 #5
    LCKurtz i cannot thank you enough, you are a excellent help!!!
     
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