MATH 210  QUIZ 3  FALL 1991

Professor Ronan Friday, November 1 – 9:00 A.M. NAME: (PRINT) SSN:

1. Evaluate ∫∫_{D} \frac{x^{2} + y^{2}}{1 + x^{2} + y^{2}} dA where D is the region in the first quadrant interior to the circle of unit radius. Thus: x^{2} + y^{2} ≤ 1, x ≥ 0, y ≥ 0.

MATH 210  QUIZ 3  FALL 1991

2. Evaluate ∫∫∫_{E} xy dV where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,2,0) and (0,0,3).

3. Find the center of mass of the volume above the paraboloid z = x^{2} + y^{2} and below the plane z = 1. Thus x^{2} + y^{2} ≤ z ≤ 1.