Set dI/dx = 0. What do you get?
Hi all, I got set this question as part of my calculus of variations homework, but the lecturer has told me that it's not actually a calculus of variations problem (just a calculus problem).
Find the minimum of the integral:
I'm not sure whether I should do something involving Leibniz's rule, or whether I should try integrating, then differentiating twice.
So far I got:
,
since
Any hints?
Correct. For finding out about min or max, try taking the second derivative and see what you get. If you can show that the second derivative is positive for the solution of the first-order DE above that you need to solve, then you've got a min. In CoV problems, I'm afraid they often don't do the second-order checking necessary to discover if you're dealing with a max or a min.