Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y = x^3, y = 0, x = 1, x = 2

Answer 1

The general formula is

V = 2π ∫ x h(x) dx

For this case the limits of the x integration are 1 and 2 and h(x) = x³ - 0

V = (2 π /5) x⁵ |₁² = 62 π /5