91Ó°ÊÓ

To find the volume of the solid generated by revolving the region around the indicated axis or line using the method of cylindrical shells, follow these general steps: 1. Identify the region and axis of rotation. 2. Determine the method for integration (with respect to x or y). 3. Set up the formula for cylindrical shells: \( V = 2\pi \int_a^b r(y)h(y)dy \) (with respect to y) or \( V = 2\pi \int_a^b r(x)h(x)dx \) (with respect to x), where r is the distance from the axis of rotation and h is the height of the shell. 4. Find the expressions for r and h in terms of x or y. 5. Set up the integral by substituting the expressions for r and h and identifying the limits of integration a and b. 6. Evaluate the integral to find the volume of the solid generated by the region when revolved around the axis or line.