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Homework Statement
Calculate the line integral:
F = <xz, (xy^{2} + 2z), (xy + z)>
along the curve given by:
1) x = 0, y^{2} + z^{2} = 1, z > 0, y: 1 → 1
2) z = 0, x + y = 1, y: 1→0
3) z = 0, xy = 1, y: 0 → 1
Homework Equations
The Attempt at a Solution
I don't think the problem is very difficult when just dividing the line integral into three parts, calculating each separately. But I want to be thorough to see if I got all the concepts.
I tried to draw the curve (see attachment) which made me realize a cone cut in half would be a capping surface, so we should be able to apply Stokes theorem. But I'm having trouble parametrizing it since we've basically dealt exclusively with very standard parametrizations.
I think that one parameter should be the height of the cone, h = [itex]\sqrt{y^{2}+z^{2}[/itex] running from 0 to 1 and the other should be the angle in the xzplane running from 0 to [itex]\pi[/itex]. I'm just having trouble setting up the variable substitution. Can anyone give me a push?
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