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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
Posted: Wed Jul 06, 2022 12:05 pm
by answerhappygod
- 2 5 Let F X Y Z X Y Z And Let S Be The Surface Obtained By Parameterizing The Surface Z X Y With 1 (310.73 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.) r(s, t) = F (†) = rs (s, t) = rt (s, t) = (s, t) × (s, t) = F(†) · (†§(s, t) × (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)