# Shells Exercises

### 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

Once again, we'll 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

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 *y* = 5.