Reeves

2020-11-03

Evaluate the surface integral

${\int}_{S}F\cdot dS$

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)=xi+2yj+3zk

S is the cube with vertices$(\pm 1,\pm 1,\pm 1)$

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)=xi+2yj+3zk

S is the cube with vertices

unessodopunsep

Skilled2020-11-04Added 105 answers

Remember that

Let's start with the top side of the cube. Along that face, the outward normal points up. I.e.

Also along the top face we have

=3(2)(2)=12 Along the left face (pretend you're sitting somewhat out on the positive

At this point hopefully you get the idea so I'm just going to quickly list the rest of the integrals and their values:

30

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