Calculus 3 Practice Test 3

Show all work and justify each step.

(1) Find where and and

(2) Find and where and and

(3)  Evaluate the double integral by converting to polar coordinates.

(4)  Evaluate the double integral by converting to polar coordinates.

(5) Given change the order of integration to

(6) Find the centroid of a homogenuous lamina that covers the region bounded by the curve and the lines and

(7) A lamina has the shape of a semicircular region Find the center of mass of the lamina if the density at each point is directly proportional to the square of the distance from the point ot the origin.

(8) Find the volume of the region that is bounded laterally by the cylinder below by the plane and above the paraboloid

(9) Evaluate where is the solid hemisphere

(10) Evaluate by using a change of variables where is the region bounded by the quarter ellipse

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