Hi guys,

I am trying to solve an integral of the form F(x,y) = Cos[ ArcTan [x,y] ]
As you imagine, the argument ArcTan[x,y] will spit out values from -pi/2 to +pi/2 as you sweep across the quadrants.
If I took this integral in polar coordinates, taking it with respect to theta - Cos(theta) - the result will be 0.

However, I can't really use polar coordinates because my field map lies in a square box. Therefore my result will be close to 0 but nonzero. Naively, I thought I could just do this:

Integral[ Cos[ ArcTan [x,y] ] , {x, -10 , 10} ] followed by Integral[ ANS, {y , -10 , 10} ]

But it doesn't seem to work. And I can't grasp why. Any insight would be really appreciated. Thanks in advance.