1. Use Green's Theorem to compute
where C is the positively oriented rectangle having vertices (0,0), (1,0),
(1,5), and (0,5).
1. Use Green's Theorem to compute
where C is the positively oriented rectangle having vertices (0,0), (1,0),
(1,5), and (0,5).
2. Compute the curl of the vector field F(x,y,z) = x2i
- exyzj + cos y k.
3. Compute the divergence of the vector field F(x,y,z) = x2i
- exyzj + cos y k.
1. Compute 
where C is the boundary of the region in the first quadrant between a circle
of radius 1 and a circle of radius 2.
2. Compute the curl of the vector field F(x,y,z) = 
.
3. Compute the divergence of the vector field F(x,y,z) =
.
[Note: Vector fields of this sort may be used to model photon flow from a star or neutrino flow from a black hole. Wow.]