# Flux through a surface Question Help Please

1. Dec 6, 2009

### leext101

1. The problem statement, all variables and given/known data
Let S be the part of the surface z=49-(x2+y2)2 above the xy-plane, oriented upward.

Let vector field F= (yz) i +(xz) j + (-17+xy) k

Compute the flux of F through S.

2. Relevant equations
Flux through surface equation ∫s F(x,y,f(x,y)) dot product (-fx i-fy j + k) dxdy

3. The attempt at a solution
I used the equation to find flux through a surface plugging in F(x,y,(49-(x2+y2)2) for the vector field, I took the dot product. I believe the limits are -sqrt(7)≤x≤sqrt(7) and -sqrt(7)≤y≤sqrt(7). The answer I integrated out was -476 which was incorrect.

I appreciate your time and help!

2. Dec 6, 2009

### rock.freak667

Try parameterizing the surface in polar coordinates and then use

∫∫F.n ds = ∫∫F |rrxrθ| dA

3. Dec 6, 2009

### HallsofIvy

The first of these should be a single path integral, not a double integral, shouldn't it? Also I am puzzled by your "F.n". I would have used $\vec{F}\cdot d\vec{s}$ where "$d\vec{s}$" is the vector tangent to the curve, not normal to it, with length ds.

4. Dec 6, 2009

### leext101

So if I do use polar coordinates would the limits be 0≤r≤sqrt(7), 0≤θ≤2∏ and a normal vector of n= k?

5. Dec 6, 2009

### leext101

using polar coordinates I calculated an answer -238pi

6. Dec 7, 2009

### leext101

If I stick with cartesian coordinates would the limits be -sqrt(7)≤y≤sqrt(7) and
-sqrt(7)≤x≤sqrt≤(7)?

Thanks everyone for posting