1. Use the Shell Method to compute the volume obtained by rotating the region enclosed by the graphs as indicated, about the y 1axis.

for y = 64 - x³, y = 64 - 16x, x ≥ 0

2. Use the Shell Method to compute the volume of the solid obtained by rotating the region underneath the graph of y = 1-x² over the interval [-1, 1] about the line x = 7.

3. Use the Shell Method to calculate the volume of rotation about the x - axis.

x = y(4 - y), x = 0

4. Let R be the region under the graph of y = 9 - x² for 0 ≤ x ≤ 2. Use the Shell Method to compute the volume of rotation of R about the x-axis as a sum of two integrals along the y -axis.

Hint: The shells generated depend on whether y ∈ [0, 5] or y ∈ [5, 9].

5. Use the Shell Method to find the volume V of the solid obtained by rotating the region above the graph of y = x² + 3 and below y = 7 for 0 ≤ x ≤ 2 about the line y = -3.

V =

6. Use the Shell Method to find the volume of the solid obtained by rotating the region below the graph of y = x² + 5 and above y = 0 for 0 ≤ x ≤ 5  about  x = 5.

V =