Stokes' Theorem

burt

Junior Member
Joined
Aug 1, 2019
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203
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This is the problem I just worked through. My problem is that, although I can't see any error, it seems to have worked out to neatly. Is this right?

Also, although I just did the work, I don't really understand what it means. If the answer is zero, does that mean the flux of a fluid on this vector field is zero? Meaning that it is not moving at all? Or that the same exact amount is coming out as is going in?
 

HallsofIvy

Elite Member
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Jan 27, 2012
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6,099
Going from (8, 0, 0) to (0, 8, 0) you have x= 8- t, y= t so dx= -dt and the first term is \(\displaystyle \int y^2 dx= t^2(-dt)\) but you have only \(\displaystyle \int t (-dt)\).
 

burt

Junior Member
Joined
Aug 1, 2019
Messages
203
This is my new answer. I think it is right.
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