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Path integral question

multint.jpg

How would you approach such a question?
Honestly? No idea - the "elliptic arcs" bit is stumping me. What are the earlier parts of the question? Do you have any idea what topic you are supposed to use to answer this?
Original post by TwiMaster
multint.jpg

How would you approach such a question?


Looks like a calculus of variations problem, but I think we need more info.
Reply 3
Original post by DFranklin
Honestly? No idea - the "elliptic arcs" bit is stumping me. What are the earlier parts of the question? Do you have any idea what topic you are supposed to use to answer this?


multint.jpg

Those are the earlier parts & I think Green's theorem may be applicable here? Don't exactly know how though
Reply 4
Isn't the integrand an exact differential?
Original post by RichE
Isn't the integrand an exact differential?
Well, I was thinking the elliptical curve thing had to be a red herriing, so it wouldn't surprise me. I can't remember what the rule is for it though, so I'll leave it in your hands :smile:
Reply 6
Original post by DFranklin
Well, I was thinking the elliptical curve thing had to be a red herriing, so it wouldn't surprise me. I can't remember what the rule is for it though, so I'll leave it in your hands :smile:


I'll wait to see if I've given hint enough.
Original post by RichE
Isn't the integrand an exact differential?


Yes, well spotted - but doesn't that make it trivial? [and PRSOM]
Original post by DFranklin
Well, I was thinking the elliptical curve thing had to be a red herriing, so it wouldn't surprise me. I can't remember what the rule is for it though, so I'll leave it in your hands :smile:


The rule for an exact differential or the elliptical curve bit? If it's the former, then it just means that the integrand is of the form df(x,y)df(x,y) for some suitable f.
Original post by atsruser
The rule for an exact differential or the elliptical curve bit? If it's the former, then it just means that the integrand is of the form df(x,y)df(x,y) for some suitable f.
OK, you made me look it up. The test where you βˆ‚x\partial x the dx term and it has to equal βˆ‚y\partial y the dy term.

Edit: as Rich has pointed out, this is the wrong way around. βˆ‚x\partial x the dy term and vice versa.
(edited 7 years ago)
Reply 10
Original post by DFranklin
OK, you made me look it up. The test where you βˆ‚x\partial x the dx term and it has to equal βˆ‚y[\partial y[ the dy term.


other way around i think
Original post by DFranklin
OK, you made me look it up. The test where you βˆ‚x\partial x the dx term and it has to equal βˆ‚y\partial y the dy term.


Right. The elliptical curve bit is misdirection, I think. [I think you swapped the derivatives though]
Original post by RichE
other way around i think
Arghh! Read the wiki page wrong. Sigh. The eye operations (March, hopefully) can't come soon enough...

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