CALCULUS 265 Honors
Instructor: Hentzel
E-mail  hentzel@iastate.edu
phone  294-8141
Tuesday, October 31:                   TEST III             


F[x,y] = (x, xy)

The path is the triangular path (0,0) to (1,0) to (0,1) to (0,0)

traversed counter clockwise. 

1.  Use Green's theorem to evaluate INT F.T ds along the path.





















2.  Use Green's theorem to evaluate INT F.N ds along the path.




































F[x,y,z] = (yz,xy,xz)


Surface is the top, bottom, and curved walls of the cylinder

x^2+y^2 = 1 from z=-1 to z=1.  N is the outward directed normal.



3.  Find   INT INT F.N dS.




























































Assume F(x,y,z) =  (x y^2, -x^2 y, z ).

S is that portion of the paraboloid z = 9 - x^2 -y^2 above the xy-plane

and N is directed upwards.   

4.  Evaluate  INT INT  F.N dS































































Let C be the intersection of the plane 1/2 y+z=1 with the cone 

z = Sqrt[x^2 + y^2].

(C is an ellipse oriented clockwise as viewed from above.)

Let F(x,y,z) = ( xy, xz, z ).


5.  Evaluate INT F.T ds