(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

calculate the upward flux of f(x,y,z) = <yz,2x+y,y^2+z>

Let S be the portion of the cylinder z=4-y^2 lying in the first octant to the right of the plane y=4.

a parametrization into the u v plane is:r(u,v)=(u,v,4-v^2)

region is a rectangle in the uv plane with bounds, (0,0) , (0,2) and (4,0)

2. Relevant equations

[tex]\int[/tex][tex]\int[/tex] F [tex]\bullet[/tex](ru [tex]\times[/tex]rv) dA

3. The attempt at a solution

ru x rv = 0i + 2vj + 1k

so then i have [tex]\int[/tex] <4v-v^3, 2u+v, v^2 + 4 - v^2 > x <0 + 2v + 1 >

[tex]\int[/tex] (2v^2 + 4uv + 4)dudv

4[tex]\int[/tex] (v^2/2 + uv + 1) dudv

i know i can't go to polar so i integrate

is this the correct integral?

0 to 2, outside integral, 4* 0 to 4 inside integral ( v^2/2 + uv + 1 ) dudv ?

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# Homework Help: Surface integrals and flux

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