2. Let C be the triangle formed by traveling from the point (0,1) to (2,1), to (2,5), and back to (0,1).
(a) (4 pts) Find a parametrization for the curve C in R².
(b) (6 pts) Evaluate the path integral of f F(x,y) = xy along the curve C.
3. (10 pts) Find the area of the part of the surface Z = 9 - x2 - y2 that lies inside the cylinder x2 + y2 = 4.
4. (10 pts) Evaluate
xy + x
where C is the arc of the ellipse x2 +42 = 1 traversed counterclockwise from (1,0) to (-1,0).
5. Let S be the part of the cone x2 = y2 + z2 that is between x = 1 and x = 3. Let S be oriented with
the normal vector pointing in the positive x-direction.
(a) (5 pts) Find an orientation preserving parametrization of the surface S.
(b) (5 pts) Let F(x,y,z) = (x,-z,-y). - Find
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