Surfaces of revolution Suppose y = f(x) is a continuous and positive function on [a, b]. Let S be the surface generated when the graph of f on [a, b] is revolved about the x-axis.
a. Show that S is described parametrically by r(u, v) = 〈u, f(u) cos v, f(u) sin v〉, for a ≤ u ≤ b, 0 ≤ v ≤ 2 π.
b. Find an
c. Apply the result of part (b) to find the area of the surface generated with f(x) = x3, for 1 ≤ x ≤ 2.
d. Apply the result of part (b) to find the area of the surface generated with f(x) = (25 – x2)1/2, for 3 ≤ x ≤ 4.
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