Find the surface integral (double integral over S) E dot dS, where S is the cylinder, x^2 + y^2 = 4, z is greater than or equal to 2 and less than or equal to 5, and the vector field F is F(x, y, z) = (0, 0, z^2)© BrainMass Inc. brainmass.com October 24, 2018, 9:28 pm ad1c9bdddf
surface integral is found. The solution is detailed and well presented.
Vector Fields and Surface Integrals
Find the flux of the vector field F(x, y, z) = (y, 0, z2) out of the unit sphere S. In other words, find the surface
integral ∫∫S (y, 0, z2) * dS, where the sphere S is oriented by the outward normal.
Let S be the cylinder x2 + y2 = 1, 0 ≤ z ≤ 6. Find ∫∫S (x4 + 2x2y2 + y4)2 dS.