# 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 = x2, 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 = x2, 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 = x2, 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 = x2, 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.