# Problem Set 20

1. Easy
Let $$S$$ be the capless cylinder $$S = \left\{(x,y): x^2+y^2=9, 0 \leq z\leq 5\right\}$$, and $$\mathbf F(x,y,z) = (2x,2y,2z)$$. Determine the flux of $$\mathbf F$$ through $$S$$.

2. Easy
Let $$S$$ be the disk of radius $$3$$, sitting in the plane $$z=3$$. Determine the flux of $$\mathbf F(x,y,z) = (0,0,x^2+y^2)$$ through $$S$$.

3. Easy
Evaluate the flux of $$\mathbf F(x,y,z) = (3x^2,2y,8)$$ over the plane $$-2x+y+z=0$$ for $$(x,y) \in [0,2]\times [0,2]$$, oriented pointing in the $$-z$$-direction.

4. Easy
Let $$S$$ be the triangle with vertices $$(1,0,0), (0,2,0), (0,1,1)$$, and $$\mathbf F(x,y,z) = (xyz,xyz,0)$$. Find the flux of $$\mathbf F$$ through $$S$$.

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