MATH 260

EXAM 3

1. (20 pt) Evaluate the following iterated integral and draw a picture of the region of integration.

2. (20 pt) Find the volume of the region bounded by the cone and paraboloid given by the equations:

3. (20 pt) Find the volume of the region bounded by the equations:

4. (20 pt) Change the following integral to spherical coordinates and evaluate (any way you like).

5. (20 pt) Find the solution to the system of equations x+y+z=6, x+y-z=0, 3x-z=0.

6. EXTRA CREDIT (10 pt) Find a formula for the area of an ellipse using a double integral (hint: recall that an ellipse is given by the equation:

with a,b>0, try the change of variables