Prepared: Wed Dec 15 14:51:08 CST 1999

MATH 1271

QUIZ X

1) Use the method of cylindrical shells to find the volume of the solid generated by rotating around the y-axis the region bounded by and y=0.

The formula to be used here is

To find the limits of the integration we find the zeros of , which are 2 and -2. It is enough to integrate only the right part of the function and then multiply by 2.

2) Find the area of the surface of revolution generated by revolving ,
around the x-axis.

The formula to be used here is

The limits are already given as 0 to 1. So