Calculate a line integral: xydS where the curve is given with |x| + |y| = 1

Question

anonymous · Answer

$$\int\limits_{?}^{?} xy dS$$                                      |x| + |y| = 1

anonymous · Answer

c'mon nikvist. :D

anonymous · Answer

So the result is zero?

nikvist · Answer

yes

anonymous · Answer

Was it necessary to get the parametric equation out of this?

anonymous · Answer

I'm trying to understand line integrals that's why I asked the queastion.

nikvist · Answer

my mistake, the answer is not correct

anonymous · Answer

oh man. well you got a medal. :)

jamesj · Answer

The answer is zero, by symmetry arguments.  

The path |x| + |y| = 1 is a diamond around the origin.  Consider this path in each quadrant.The first quadrant integral cancels the second quadrant as for every xy ds in Q1 has an equal and opposite -xy ds in Q2 (as x -> -x).  The same can be said for Q3 and Q4.

anonymous · Answer

Is this correct?