Euler-Lagrange for summation of integrations

Given integration

E = \int_{a}^{b} A(x,y,y')dx

Using Euler - Lagrange equation we can find the necessary condition for
an extremum

dA/dy-d/dx dA/dy' = 0

Now consider two integrations with two different limits

E = \int_{a}^{b} A(x,y,y')dx + \int_{c}^{d} B(x,y,y')dx

What would be the corresponding Euler lagrange equation(s)? Is it
simply the following?

dA/dy-d/dx dA/dy' = 0
dB/dy-d/dx dB/dy' = 0

Or in a single equation

dA/dy-d/dx dA/dy' + dB/dy-d/dx dB/dy' = 0

Any help or pointers to books is highly appreciated.
Thanks

.

Relevant Pages

  • Re: Euler-Lagrange for summation of integrations
    ... Using Euler - Lagrange equation we can find the necessary condition for ... What would be the corresponding Euler lagrange equation? ... In general, if the ranges of the integrals are I and J, we use the ...
    (sci.math)
  • Re: Is RK5 better than RK4 in this situation ??
    ... version) as an integral part of a complex analytical method. ... let us assume that there is no bug in your RK4: ... if you observe that the four K_i in one integration step vary drastically, ... there this occurs (with Euler, you are looking back at one point only ...
    (sci.math.num-analysis)