My working continued...
(b) Multiplying with , integrating in yields
Then integration by parts in (A) yields
Using that and
Substituting this back into (A) yields
I'm not sure how to continue here.........
I have another question involving extremals. There are 3 parts to it, and trickier than my last post.
(a) Find the extremal for
(b) For the extremal show that
(c) Prove that is a minimizing curve.
My Working (haven't made much progress)
(a) Applying the Euler-Lagrange equation
which has solution
which is really as far as I've gotten so far. What's throwing me off is the in the value of . I'm not sure how to handle this.