#Question about Greens Theorem

19 messages · Page 1 of 1 (latest)

waxen hill
calm yarrowBOT
waxen hill
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Oh shoot wrong picture

buoyant tiger
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@waxen hill post the right picture lol

waxen hill
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@buoyant tiger

buoyant tiger
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do you just want the line integral of r(t) through a vector field?

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I'm inclined to say you could use green's theorem on the loop and then subtract off the line integral of the line from (-3,0) to (3,0)

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since greens theorem allows us to say that the circulation along a simple closed loop is equal to the curl contained within the loop

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we'd be getting the circulation along the loop and then just subtract off the part of the loop we don't want

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so we'd want something like this

image.png
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which is a piecewise smooth simple closed curve

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so this is how you'd evaluate that

image.png
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wait hold on

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sorry I made a mistake

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it should be del cross F not del dot F

waxen hill
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oh its curl F?