Consider the sphere, x^2 + y^2 + z^2 = 2, and the paraboloid z = x^2 + y^2. Requried:
a. Describe the intersection of the sphere and the paraboloid in terms of a pair of equations.
b. Write down the iterated triple integral in cylindrical coordinates that represents the volume of the region bounded above by the sphere and below by the paraboloid. Hence evaluate this volume.
c. Write down the iterated triple integral in spherical coordinates that represents the volume of the region defined in (b). Do not evaluate this integral.