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Surface Integral of quartercylinder 
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#1
Sep3010, 08:56 PM

P: 12

1. The problem statement, all variables and given/known data
I am taking the surface integral over a quarter cylinder. Everything is fine and I can get the correct answer, it's just a conceptual problem that I need help with. 2. Relevant equations The da for the "curved" outer surface is [tex]da=sd\phi dz\hat{s}[/tex] The da for the bottom surface is [tex]da=sdsd\phi (\hat{s})[/tex] I understand why the curved da is multiplied by s, since we are integrating over a surface that is projected into 3space by a distance s. I do not understand why this s occurs in the da for the bottom (and top) surface. We integrate over a dynamic ds to find the surface integral for this piece....so why multiply the differential area by s? 


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