1. The problem statement, all variables and given/known data Vector field ##\vec F= 4x \hat i+4y \hat j +3 \hat k## Let S be the open surface above the xy-plane defined by ##z=4-x^2-y^2## a. Evaluate normal outward flux of F through S. b. Use Stokes' theorem to evaluate the normal outward flux of ##∇ \times \vec F## through S. c. Use Gauss' theorem to evaluate the volume integral $$\iiint_V (∇\times \vec F)\,. dxdydz$$ where V is the volume enclosed by S and the xy-plane. 2. Relevant equations vector field, curl, div, flux formula, etc. 3. The attempt at a solution Part (a): First, i found the unit normal vector, ##\hat n## and then i used the formula: $$\iint_S \vec F. \hat n .dS$$ Is that correct? I calculated the integrand and then projected on the xy-plane for the surface area. Part (b): I used the following formula: $$\iint_S ∇\times F. \hat n .dS$$ Is that correct? If yes, then for this part i got the curl F = 0, so i didn't calculate the rest as the double integral of 0 is 0. Part (c): I used the formula: $$\iiint_V ∇. F .dxdydz$$ I found div F, then used cylindrical coordinates to find the volume. I'm quite sure that i got this part right.