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Derivative of Definite Integral Conundrum

  1. Sep 9, 2016 #1
    1. The problem statement, all variables and given/known data

    The normal approach using the fundamental theorem of calculus seems inapplicable. I define a function B(R) based on a definite integral with one of the limits being R. One factor in the definite integral has R in it and that function vanishes to 0 at x = R.

    Using the fundamental theorem I run into the problem that the derivative of B(R) evaluates to 0.

    2. Relevant equations
    upload_2016-9-9_15-48-38.png


    K is just a constant greater than R.

    3. The attempt at a solution

    Reversing the sign and the limits of integration is as far as I got. If I do a straight replacement of x with R, Cos-1(R/x) goes to Cos-1(1) which is zero...

    I'm trying to isolate G but this has me stumped.
     
  2. jcsd
  3. Sep 9, 2016 #2

    andrewkirk

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    Try writing the two occurrences of ##R## in the formula as separate variables ##u## and ##v## and write ##B(R)## as a function of the two variables, each of which is a function of ##R##, viz: ##u(R)=V(R)=R##.

    If you can do that then you can then use the total derivative formula to find ##\frac{dB}{dR}##.
     
  4. Sep 9, 2016 #3

    Ray Vickson

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    Have you forgotten (or perhaps, never learned) Leibniz' (Integral) Rule? See, eg.,
    http://mathworld.wolfram.com/LeibnizIntegralRule.html
     
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