**1.** The purpose of choosing a coordinate system other than the obvious
rectangular coordinates is to simplify the integral. This is achieved if the
region or surface becomes simple in the new coordinate system, and/or if the
integrals obtained become doable.

When there is no obvious simplification one can always start with rectangular
coordinates.

**2.** Other coordinates which can be kept in mind are polar (in two dimensions),
cylindrical and spherical. Variations in the latter which involve scale changes
are called ellipsoidal coordinates. When your region is bounded by certain surfaces,
you can conceivably use the functions that define these surfaces as variables.