Suppose that the parametrized curve C: ((u), g(u)) is revolved about the x-axis, where g(u) > 0

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Suppose that the parametrized curve C: (ƒ(u), g(u)) is revolved about the x-axis, where g(u) > 0 for a ≤ u ≤ b.


a. Show thatimage


is a parametrization of the resulting surface of revolution, where 0 ≤ ν ≤ 2π is the angle from the xy-plane to the point r(u, ν) on the surface. Notice that ƒ(u) measures distance along the axis of revolution and g(u) measures distance from the axis of revolution.image


b. Find a parametrization for the surface obtained by revolving the curve x = y2, y ≥ 0, about the x-axis.

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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