Differential under an integral sign.

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  • #1
binbagsss
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Sorry I'm not sure how you get math script on here, so have had to attach it.

It is a differential under an integral sign and I'm not too sure how to approach it.
Would you use Leibniz rule?
Do you differentiate or integrate first?
- where y is a function of x, and R of y

Thanks in advance
 

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Answers and Replies

  • #2
STEMucator
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You don't need to integrate here.

You have y as a function of x and R as a function of y. You want to find the partial of R with respect to y which you know is a function of x. So when you differentiate the integrand, don't forget to apply the chain rule.
 
  • #3
vanhees71
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No! What's asked for is the functional derivative. You get it by evaluating, how the integral changes when the function [itex]y(x)[/itex] changes by an infinitesimal [itex]\delta y(x)[/itex]. Unfortunately the problem is not completely stated. You also need boundary conditions. If it's a usual variational problem like in Hamilton's principle, the values at the end points are fixed.
 

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