# Integrating with Polar Coordinates Exercises

### Example 1

Write an integral expression for the area for the shaded region below

### Example 2

Write an integral expression for the area for the region below the *x*-axis and above the graph of the polar function *r* = sin *θ* – 1

### Example 3

Write an integral expression for the area of one petal of the graph of the polar function *r* = sin(3*θ*)

### Example 4

Write an integral expression for the area of one petal of the graph of the polar function *r* = cos(2*θ*)

### Example 5

Write an integral expression for the area of the intersection of the regions enclosed by *r* = sin *θ* and *r* = cos *θ*

### Example 6

Write an integral expression for the area

between the graphs *r* = sin *θ* and *r* = 2sin *θ*

### Example 7

Write an integral expression for the area of the shaded region below.