Reference no: EM13844332
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 =
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