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I am a little bit confused when it comes to finding the Euler Lagrange equation of the Jacobi equation

$$J(\phi) = \int^b_a f_{uu}\phi^2 + f_{uv}\phi \phi_x + f_{vv}\phi_x^2$$

The Euler Lagrange equation is $$J_\phi - \frac{d}{dx} J_{\phi_x} = 0$$ How do I deal with taking the derivative of $J$ with respect to $\phi$ under the integral?

  • See page 48 here: {https://www.amazon.com/Numerical-Mathematics-Stochastic-Modelling-Probability/dp/0387906142/ref=sr_1_1?s=books&ie=UTF8&qid=1495208696&sr=1-1&keywords=9780387906140#reader_0387906142} – avs May 19 '17 at 15:46
  • I do not have access to that book. I do not want to sound rude, but could you briefly explain here please? () –  May 19 '17 at 16:36
  • You are not rude, but, unfortunately, I don't have time to explain here. You may not have the book, but the "Look Inside" option on the Amazon allows you to look at the needed page.

    Alternatively, see the "Derivation of one-dimensional Euler–Lagrange equation" here: {https://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation}

     – avs May 19 '17 at 18:15
  • Is this an exercise taken from a textbook? – Qmechanic May 24 '17 at 16:30

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