Flux through a surface Question

[leext101]

Homework Statement

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.

Homework Equations

Flux through surface equation ∫_s F(x,y,f(x,y)) dot product (-f_x i-f_y j + k) dxdy

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!

 

[rock.freak667]

Try parameterizing the surface in polar coordinates and then use

∫∫F.n ds = ∫∫F |r_rxr_θ| dA

 

[HallsofIvy]

Try parameterizing the surface in polar coordinates and then use

∫∫F.n ds = ∫∫F |r_rxr_θ| dA

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.

 

[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?

 

[leext101]

using polar coordinates I calculated an answer -238pi

 

[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