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August 27th, 2017, 06:12 AM   #1
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Divergence theorem - confused over here

Okay so I found two solved examples (attached).

The first one says:
F (x, y, z) = (y, −x, z) and P is the bottom part of the surface: z^(x^2+y^2), x^2+y^2<2. Find the flux.

The second one says: F(x,y,z) = (z*e^(y^2), x^2+1, z). P is bottom part of the spherical cap: x^2+y^2+(z-5)^2=25, z>8 Find the flux.

But they are solved differently. The first one is oriented with (0,0,1) and second one with (0,0,-1). Also the formula is different. And now I'm confused why?
Attached Images
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File Type: jpg 2lalalaCapture.jpg (19.2 KB, 5 views)
File Type: jpg 3lalalaCapture.jpg (17.5 KB, 4 views)
File Type: jpg 4lalalaCapture.jpg (7.1 KB, 4 views)
File Type: jpg 333333333333Capture.jpg (11.5 KB, 3 views)

Last edited by sarajoveska; August 27th, 2017 at 06:22 AM.
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