1. (M) Let R be the region enclosed by the ellipse x2 + 4y2 = 4. Using an appropriate change of variables to evaluate JJpy dA. Make sure you specify the change of variables and draw the new region. 2. (M) Find the volume V of the solid region D bounded above by z = 5 on the sides by the paraboloid z = 16 - x2 - y and below by the xy-plane. 3. (M) Evaluate S. F.dr where F = xyi + 2zj + (y + 2)k where C is composed of the line segments from (0, 0, 0) to (0, -1,0) and from (0, -1, 0) to (1, 1, 2) 4. (W) Evaluate Jo(et +y) dx + (x + 2y) dy where C is any piecewise smooth curve in the ry-plane from (0, 1) to (2, 3). 5. (W) Use Green's theorem to evaluate fay + ydx + 3y xdy where C is the circle a2 + y = 100 oriented counterclockwise. 6. (W) Let E be the semi-ellipsoid z = 4V1 -x2 - y2 oriented so that the normal is directed upward and let F = x2i+ y'j + z2 tan(xy)k. Compute ff,, curl(F).ndS (Hint: Use Stokes' theorem twice so that you express the required integral as the integral over a different region over which the quantities are easier to integrate)