Interchanging order of integration in spherical coordinates

 As we saw before the order of integration can be changed. We use an example to show that.

Example

Let E be the region bounded below by the cone z = ⎷x² + y² and above by the sphere z = x² + y² + z².Set up a triple integral in spherical coordinates and find the volume of the region using the following orders of integration.

a. dρdഴdθ

b. dഴd𝜌dθ

Solution