IrishBoy123
  • IrishBoy123
Orientation Question: re-calculus of variations
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
IrishBoy123
  • IrishBoy123
if we have \(I = \int_a^b \; dx \sqrt{1 + y'^2}\) what are \(\dfrac{dI}{dy}\) and \(\dfrac{dI}{dy'}\) ??
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle f(x)=\int_{a}^{b}g(t)~dx }\) \(\large\color{#000000 }{ \displaystyle F(x)=G(a)+G(b) }\) (F'=f) \(\large\color{#000000 }{ \displaystyle f'(x)=0 }\) (i suppose that would be for d\(\rm I\)/dy)
SolomonZelman
  • SolomonZelman
because \(I\) is constant when evaluated at constant limits [of integration], and the derivative of a constant, blah blah blah. ....

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SolomonZelman
  • SolomonZelman
or is it something different? I am becoming afraid
IrishBoy123
  • IrishBoy123
soz, Sol y = y(x)
SolomonZelman
  • SolomonZelman
ooh
SolomonZelman
  • SolomonZelman
you have y' sitting in there didn't see the '
SolomonZelman
  • SolomonZelman
I haven't learned that yet -:(
SolomonZelman
  • SolomonZelman
Hopefully, the time comes though ...
SolomonZelman
  • SolomonZelman
(please remove the medals)
SolomonZelman
  • SolomonZelman
I will play around and see if it is possible to solve this via some elementary calc that I know..
SolomonZelman
  • SolomonZelman
probably not... (I wrote down and I will look at some maths.... perhaps that would be a motivation, but you need someone much more knowledgable than a guy) my apologizes and good luck...

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