# Flux Integrals

## Homework Statement

Compute the flux of the vector field, , through the surface, S.
$$\vec{F}$$= 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
$$\int$$F(x,y,f(x,y)$$\circ$$<-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
$$\int$$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?