# Area, Volume, and Arc Length

### Example 1

Let *R* be our favorite region.

Use the shell method to write an integral expression for the volume of the solid obtained by rotating *R* around the line

*x* = 2

### Example 2

Let *R* be our favorite region.

Use the shell method to write an integral expression for the volume of the solid obtained by rotating *R* around the line

*y* = 1

### Example 3

Let *R* be the region in the first quadrant bounded by the graph *y* = *x*^{2}, the *y*-axis, and the line *y* = 4. Use the shell method to write an integral expression for the volume of the solid obtained by rotating *R* around

the *y*-axis

### Example 4

Let *R* be the region in the first quadrant bounded by the graph* y* = *x*^{2}, the *y*-axis, and the line *y* = 4. Use the shell method to write an integral expression for the volume of the solid obtained by rotating *R* around

the line *x* = -1

### Example 5

Let *R* be the region in the first quadrant bounded by the graph *y* = *x*^{2}, the *y*-axis, and the line *y* = 4. Use the shell method to write an integral expression for the volume of the solid obtained by rotating *R* around

the *x*-axis

### Example 6

*R* be the region in the first quadrant bounded by the graph *y* = *x*^{2}, the *y*-axis, and the line *y* = 4. Use the shell method to write an integral expression for the volume of the solid obtained by rotating *R* around

the line *y* = 5