Question

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

Answer 1

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

Answer 2

c'mon nikvist. :D

Answer 3

So the result is zero?

Answer 4

yes

Answer 5

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

Answer 6

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

Answer 7

my mistake, the answer is not correct

Answer 8

oh man. well you got a medal. :)

Answer 9

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.

Answer 10

Is this correct?