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Divergence Theorem:: Find the flux of F = ( cos(z) + xy^2, xexp(-z), sin(y)+x^2z )
Автор: Jonathan Walters
Загружено: 2019-11-25
Просмотров: 6200
Описание:
Find the flux of F = ( cos(z) + xy^2, xexp(-z), sin(y)+x^2z ) outward through the surface which encloses the region bounded by the paraboloid z=x^2+y^2 and the plane z=4.
Here we take the divergence of the field F then integrate that over the solid region enclosed by the surface.
We use cylindrical coordinates here because of the circular symmetry around the z axis.
We continuously use the fact that z=x^2+y^2 = r^2 in cylindrical coordinates.
Thanks for watching and as always if you have any questions, feel free to ask in the comments!
-dr. dub
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