2. (5) Let F(x, y, z) =< x², y², z>, and let S be the surface obtained by parameterizing the surface z=x²-y2, with 0≤x≤

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2 5 Let F X Y Z X Y Z And Let S Be The Surface Obtained By Parameterizing The Surface Z X Y2 With 0 X 1 (37.16 KiB) Viewed 13 times

2. (5) Let F(x, y, z) =< x², y², z>, and let S be the surface obtained by parameterizing the surface z=x²-y2, with 0≤x≤ 1 and 0 ≤ y ≤ 2, so that the normal to the surface has a positive k component. (Note to avoid a super common mistake: the 3rd component of F is z, not z². For some reason, students want to square their z. Don't.) 7(s, t) = F(F) = 7,(s, t) = 7,(s, t) = (s, t) x (s, t) = F(F) (F(s, t) x (s, t)) = So the flux is (write the integral, get the sign correct, do the integral): (include limits!) (this is a vector) (this is a scalar)