Question

Evaluate the surface integral Evaluate the surface integral S F · dS for the given vector...

Evaluate the surface integral

Evaluate the surface integral
S

F · dS

for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = x i + y j + 9 k


S is the boundary of the region enclosed by the cylinder

x2 + z2 = 1

and the planes

y = 0 and x + y = 8

F · dS

for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = x i + y j + 9 k


S is the boundary of the region enclosed by the cylinder

x2 + z2 = 1

and the planes

y = 0 and x + y = 8

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