1. Triple Integrals in Spherical and Cylindrical In rectangular coordinates: dV = dzdydx In cylindrical coordinates: dV = r dzdrdθ In spherical coordinates: dV = ρ 2 sin φ dρdφdθ

2. Cylind  RectRect  Cylind Spher  RectRect  Spher

3. Ex. Sketch the solid whose volume is given by the integral

4. Ex. Evaluate

5. Ex. A solid lies within the cylinder x 2 + y 2 = 1, below the plane z = 4, and above the paraboloid z = 1 – x 2 – y 2. The density at a point is proportional to its distance to the z-axis. Find the mass.

6. Ex. Evaluate, where B is the unit ball.

7. Ex. Find the volume of the solid that lies above and below x 2 + y 2 + z 2 = 9.