F(x, y, z) = A(x + y4)ỉ + B(2,5 + y)j + C(x2 + y2)k


where A = 1, B = 0.2, and C = 1 are constants.


Compute the following:


a. Integrate F around the rectangle defined by the points (2,1,0), (3.2,1,0), (3.2,4.1,0), and (2,4.1,0).

b. Integrate F around a circle on the x-y plane of radius 7.1, with the center at the origin.

c. Integrate F over the surface of a rectangular prism defined by the points given in Part (a) and extruded in the positive k direction by a distance 0.4.

d. Integrate F over the surface of a cylinder defined by the circle given in Part (b) and extruded in the positive k direction by a distance 0.4.