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May 26th, 2017, 08:57 AM   #1
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Question Line Integral: intersection of sphere and cylinder

Vectorial Field: F(x, y, z) = (y², z², x²)

Sphere: x² + y² + z² = a²
Cylinder: x² + y² = ax

z<=0 ; a>0

How to parametrize the curve?? The exercise says it's clockwise when seen by the xy plan
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May 26th, 2017, 01:58 PM   #2
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I would start by using the standard parameterization for a sphere pf radius a (spherical coordinates):




Then and so that . And, from that, .

Putting those together


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Last edited by Country Boy; May 26th, 2017 at 02:42 PM.
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May 27th, 2017, 01:27 PM   #3
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Quote:
Originally Posted by Country Boy View Post
I would start by using the standard parameterization for a sphere pf radius a (spherical coordinates):




Then and so that . And, from that, .

Putting those together


Great! But.. The integral will be VERY laborious.. Any thoughts?
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