# Derivative of Definite Integral Conundrum

1. Sep 9, 2016

### ObjectivelyRational

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

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. Sep 9, 2016

### andrewkirk

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 $\frac{dB}{dR}$.

3. Sep 9, 2016

### Ray Vickson

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