Question 1:

Evaluate p y'dx - x'dy, where C is the boundary of the region between the circles C x2 + y? = 25 and x2 + y = 36Use Green's Theorem to evaluate f 13" - d where 131:1}, y) = (6:33;, 3/4 + 3) and C is the C rectangle with vertices (3,5), (8,-5), (8,8), and (3,8). The integral obtained from from Green's Theorem is MW where D is the interior of the rectangle. This evaluates to 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 (x, -xy'), out of the rectangle with vertices (0,0), (4,0), (4,6), and (0,6)