[積分] Surface Integrals

[hwujialuen (松原拓)]

           Evaluate the surface integral


1       ∫ ∫xy dS
         S

         S is the boundary of the region enclosed by the cylinder

  x^2 +z^2=1 and the planes y=0 and x+y =2





2          Evaluate the surface integral ∫ ∫F dS
                                          S

          F(x,y,z)=yj -zk

          S consists of the paraboloid y= x^2 +z^2 ,0<y<1 ,and the

 disk x^2 +z^2 ≦1 ,y=1



3         ∫ ∫(x^2 +y^2 +z^2)dS
           S

         S consists of the cylinder in Exercise 10 together with

         its top and bottom disks

         Exercise10: S is the part of the cylinder x^2 +y^2=9

                     between the planes z=0 and z=2

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