Problem $3$

Consider a circle of radius $2$ centered at the origin, and a velocity field given by

$v=(x-y)i+(x+y)j$

a$)$ Compute the divergence of the velocity over the disk

b$)$ Compute the contour integral of velocity dotted with the disk's outward unit normal

c$)$ From the divergence theorem, the two results above should be equal. Verify this is what you got.