# Area, Volume, and Arc Length

# Integrating with Polar Coordinates Exercises

### Example 1

Write an integral expression for the area for ...

the shaded region

### 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 for ...

one petal of the graph of the polar function *r* = sin(3θ)

### Example 4

Write an integral expression for the area for ...

one petal of the graph of the polar function *r* = cos(2θ)

### Example 5

Write an integral expression for the area for ...

\item 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