Chapter 6.11, Problem 2P

Given the vector $A=\left(x^2-y^2\right)i+2xyj.$

(a) Find $\nabla \times A$

(b) Evaluate ${\displaystyle \iint (\nabla \times A)}\cdot d\sigma$ over a rectangle in the $(x,y)$ plane bounded by the lines $x=0,x=a,y=0,y=b.$

(c) Evaluate ${\displaystyle \oint A}\cdot dr$ around the boundary of the rectangle and thus verify Stokes' theorem for this case.