   Chapter 16.6, Problem 29E

Chapter
Section
Textbook Problem

Find parametric equations for the surface obtained by rotating the curve y = 1/(1 + x2), −2 ⩽ x ⩽ 2, about the x-axis and use them to graph the surface.

To determine

To find: The parametric equations for the surface obtained by rotating the curve y=11+x2,2x2 , about the x-axis and to graph the surface.

Explanation

Given data:

The surface is obtained by rotating the curve y=11+x2,2x2 , about the x-axis.

Formula used:

Write the expression for parametric equations when the surface is obtained by rotating the curve y=f(x),axb about the x-axis.

x=x,y=f(x)cosθ,z=f(x)sinθ,axb,0θ2π (1)

Here,

θ is the angle of rotation about the x-axis.

Calculation of Parametric equations of the surface:

As the surface is obtained by rotating the curve y=11+x2,2x2 , about the x-axis, substitute 11+x2 for f(x) and apply the limits of x-parameter in equation (1) as follows

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