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Chapter 6: Q. 55 (page 512)

Consider the region between the graph of f(x) = 1 鈭� cos x and the x-axis on [0,蟺]. For each line of rotation given in Exercises 55鈥�58, write down definite integrals that represent the volume of the resulting solid and then use a calculator or computer to approximate the integrals.

Short Answer

Expert verified

The volume of the resulting solid is V=14.804.

Step by step solution

01

Step 1. Given

The graph of f(x) = 1 鈭� cos x and the x-axis on [0,蟺].

02

Step 2.  Calculation

The given region bounded by f(x)=1-cos x and x-axis, between the interval [0,]is rotated around the x-axis, y=0. The objective is to determine the volume of solid of revolution using definite integrals.

The radius of each disk is given as f(x).

V=蟺鈭�ab(f(x))2dx

The total volume of solid is determined by

Use this definition and the values determined above to determine the volume of solid of

revolution.

V=蟺鈭�ab(1-cosx)2dx

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