Consider the function f (x, y) = xy integrated over a square region in the xy plane centered at the origin.

a. Draw contours of constant f values (positive and negative) in the plane and decide whether the integral can have a nonzero value. Any square region centered at the origin will have equal positive and negative contributions to the integral. Therefore the value of the integral is zero.

b. Use the information that the square has D_4h symmetry and determine which representation the integrand belongs to. Decide whether the integral can have a nonzero value from this information.