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Surfaces of revolution Let C be the curve x = f(t), y = g(t), for a ≤ t ≤ b, where f′ and g′ are continuous on [a, b] and C does not intersect itself, except possibly at its endpoints. If g is nonnegative on [a, b], then the area of the surface obtained by revolving C about the x-axis is
Likewise, if f is nonnegative on [a, b], then the area of the surface obtained by revolving C about the y-axis is
(These results can be derived in a manner similar to the derivations given in Section 6.6 for surfaces of revolution generated by the curve y = f(x).)
111. A surface is obtained by revolving the curve x = e3t + 1, y = e2t, for 0 ≤ t ≤ 1, about the y-axis. Find an
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Calculus: Early Transcendentals (3rd Edition)
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