- #1
madcattle
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Homework Statement
F= xi + x3y2j + zk
C is the boundary of the semi-ellipsoid z=√(4-4x2-y2) in the plane z=0
Homework Equations
Stokes theorem states:
∫∫(curlF ° n)dS
The Attempt at a Solution
I found the curl of the F to be 3x2y2k
I found that the dot product of CurlF and n = 3x2y2 divided by dS
Then,
∫∫(3x2y2)/(dS)*dS
=∫∫(3x2y2)dxdy
I evaluated this integral on Wolfram Alpha with the following boundaries:
y goes from -√(4-4x2) to √(4-4x2)
and x from -1 to 1 and got the correct answer = ∏
However, I am finding it impossible (for me!) to do the integral by hand and am wondering if someone can help me turn this into polar coordinates or something else that makes it more solvable
Thank!