#### Example 1.

Suppose we are given

(1)

where is the region bounded by portion of the unit disk in first quadrant. We know

(2)

and since

(3)

we can write

(4)

#### Example 2.

Suppose we want to evaluate the integral

(5)

We begin by drawing the region

We use polar coordinates as

(6)

and so

(7)

Take a close look at this integral and make sure it makes sense. Then compute it.