Question 1:

Use Green's Theorem to evaluate / F - ds, where C F= 2 C is the boundary of the region enclosed by y = 3:1: :1: and the x-axis (oriented positively). Compute the flux of the vector field ( a, -xy ), out of the rectangle with vertices (0,0), (4,0), (4,6), and (0,6)If C is a circle of radius 4 centered at the point ( 0, 3 ), then evaluate f3 (3y 3511193)) d3: + (63: sin (3/3 + y))dy. value = 115' ' (Note: the factor of 71' is already there!)