Question

Q2 13 Points Begin with the paraboloid = 22 + y2, for 0 < < 4, and slice it with the plane y 0. Let S be the surface that remains for y> 0 (excluding the planar surface in xz-plane) oriented downward (i.e. n3 <0). Let C be the Semicircle and the line segment in the plane z = 4 with counterclockwise orientation and F =< 2x + y, 2x + z, 2y + x>. ZA с S 2 = x² + y² . Q2.1 8 Points Evaluate directly SI(V F). ñ ds. You can't use any theorem) Please select file(s) Select file(s) Q2.2 5 Points Now let S = {(x,y,z) : y=0, 22 < < 4}, the flat part of the solid, oriented outwards (i.e. 12 <0). Assuming that Ss, (V x F). ñ ds = 32/3, evaluate fc F. dr, and explain the connection with the previous answer. (Hint: Use Stokes Theorem)

Answer 1

ss (supoños. ch رمان لم لا dz 2af2 22ty 2y + x 1(2-1)-3 (1-2)+6 (2-1) Magta? ń: 2wirzyj Vintag! tn 22+24 It (2231 crys dady Nun seigt 5 ] (ecruorosta (2644010342 Cacino) -1 ) e dado OnaD IÀ Ricaso +2rsino-rdado Plan (prinos + 2(]cnosti ja O - 2 ñ 2*812) 2. 32 3 (2.2 2012 from Stokes theorem, ſ Bfar frids i da S,+8 93-2+1-3})= = -2,