Area, Volume, and Arc Length

Example 1

Write an integral expression for the area for ...

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