1. (25) Let F(x, y, z) =< x², y², z >, and let S be the surface obtained by parameterizing the surface z = y² - 2x², wit

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1 25 Let F X Y Z X Y Z And Let S Be The Surface Obtained By Parameterizing The Surface Z Y 2x Wit 1 (93.16 KiB) Viewed 52 times

1. (25) Let F(x, y, z) =< x², y², z >, and let S be the surface obtained by parameterizing the surface z = y² - 2x², with 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2 (there is a rectangle sitting under our surface!), so that the normal to the surface has a positive component. r(s, t) = (Uses and t. Show the limits.) rs (s, t) = rt(s, t) = r(s, t) × (s, t) = F(ř) F (†) = F(†) · (†(s, t) × (s, t)) = 45³ − 2t³ +1²-25² So the flux is (write the integral, get the sign correct, do the integral): (that's what you better get!!)