test help!1)Set up a double integral for calculating the flux of F⃗ =3xi⃗ +yj⃗ +zk⃗ through the part of the surface z=−5x−2y+4 above the triangle in the xy-plane with vertices (0,0), (0,3), and (2,0), oriented upward.

Flux = ∫BA∫DC

A =
B =
C =
D =

Flux = ∬SF⃗ ⋅dA⃗ =

Question

test help!1)Set up a double integral for calculating the flux of F⃗ =3xi⃗ +yj⃗ +zk⃗  through the part of the surface z=−5x−2y+4 above the triangle in the xy-plane with vertices (0,0), (0,3), and (2,0), oriented upward. 


Flux = ∫BA∫DC      

A =  
B =  
C =  
D =  

Flux = ∬SF⃗ ⋅dA⃗  =

anonymous · Answer

Are you familiar with Electricity and Magnetism Physics?

anonymous · Answer

First let's think of the definition of flux,  it is noted by $$\phi _{0} = EA cos(\theta)$$

anonymous · Answer

You find dA for the the plane, you find $dA= \sqrt {30} $

anonymous · Answer

You find the normal upward vector to the plane (5,2,1)

anonymous · Answer

You find (5,2,1) dot ( 3 x , y, -5 x - 2 y + 4)=4 + 10 x

anonymous · Answer

$$
\int_0^2 \left(\int_0^{3-\frac{3 x}{2}}
   \sqrt{30} (10 x+4) \, dy\right) \,
   dx=32 \sqrt{30}
$$

anonymous · Answer

The bound are for the triangle in the xy plane