Homework #13 (the last one!)

Do all integrals
entirely by hand showing all the steps, except where noted otherwise. 
You may, if you wish, check your calculations with Maple.


15.3    Fundamental theorem and path-independence
        16. (a) Show that F is conservative and then find a potential for it.
	(b) Find the tangential line integral of F along
	some curve in the first quadrant that starts at (1,1) and ends at (4,27).
	Don't do any further integration!
 
15.5    14. Compute the flux of a vector field through a surface.

	18. Ditto.

15.6    1. Verify the divergence theorem in an example.

15.7    1. Use Stokes' theorem in an example.