- #1
Orson1981
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Homework Statement
This comes from Mathematical Methods for the Physicist from Susan Lea, Chapter 1 Question 25 Part B (Incase anyone is familar with the book). The question asks to evaluate the line integral
integral (u*dl)
where the vector u is:
u = x*y^2 i + y*x^2 j
along the path of a semi-circle in the xy plane with a radius of a and the flat side of the semi-circle along the x-axis
Homework Equations
see below
The Attempt at a Solution
I am near certain the answer is 0, evaluating this in polar coor. gives me 0 and taking advantage of the del operator to find the surface integral gives me 0, so two methods out of three give me zero.
however when I evaluate the integral in cartesian cord. I end up with 1/4 * a^4 for the half circle path and 0 for the bottom path. I am almost sure that the bottom path should not be zero for this to work, but I have no idea how to find it.
My sanity really depends on knowing how I messed this up, because it looks so good on my paper :)
Anyways, thanks for the help
PS. Anyone know a good way I can enter equations onto the forums, I don't think typing it this way really makes the situation clear.
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