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Flux Integrals

  • Thread starter theown1
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  • #1
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Homework Statement



Compute the flux of the vector field, , through the surface, S.
[tex]\vec{F}[/tex]= 3xi + yj + zk and S is the part of the surface z + 4x + 2y = 12 in the first octant oriented upward.

Homework Equations


by definition from my book the integral is
[tex]\int[/tex]F(x,y,f(x,y)[tex]\circ[/tex]<-fx,fy,1>dxdy

for a plane oriented up

The Attempt at a Solution



So to get f(x,y) from the surface i did
z=f(x,y)=12-4x-2y

I have to find the integral of the vector field dot product with <-fx,-fy,1> which turns out to be <4,2,1>

So <3x,y,12-4x-2y>dot<4,2,1>=8x+12

Next I have to find
[tex]\int[/tex]8x+12dxdy

I'm not sure what to set my values at to solve this, I tried 0<x<3 and 0<y<6
With those values my integral equaled 288 which was the wrong answer
then I tried to dot the first part with <-4,-2,1> and my answer was -432 which was still wrong

Can someone help me find the integration values for the first octant of that plane, I think thats all I need to solve this?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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618
The xy domain is a triangle, it's bounded by x=0, y=0 and the line 0=12-4x-2y, isn't it? 0<x<3 and 0<y<6 is a rectangle.
 

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