- 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 (219.18 KiB) Viewed 48 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) = = r(s, t) = rt (s, t) = (s, t) × (s, t) = (Use s and t. Show the limits.) ₹ (†) = F(r) · (ř§(s, t) × řt(s, t)) = 4s³ − 2t³ + f² − 25² - So the flux is (write the integral, get the sign correct, do the integral): (that's what you better get!!)