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Chapter 6: Q. 11 (page 575)

The volume of the solid obtained by revolving the region between the graphs of f(x)=x and g(x)=x3 on 0,1 around (a) the y-axis and (b) the line x=2.

Short Answer

Expert verified

(a) The volume is 25蟺cubic units.

(b) The volume is1915蟺cubic units.

Step by step solution

01

Volume around y-axis

The required region is shown below,

y=x鈬�x=y2y=x3鈬�x=y1/3

The volume is computed as,

V=蟺鈭�01y2/3-y4dy=蟺35y5/3-y5501=蟺35-15=25蟺cubicunits

02

Volume around line x=2

The outer radius is 2-y2.

Inner radius is 2-y1/3.

The volume is computed as,

V=蟺鈭�01(2-y2)2-(2-y1/3)2dy=蟺鈭�01y4-4y2-y2/3+4y1/3dy=蟺y55-43y3-35y5/3+3y4/301=蟺15-43-35+3=1915蟺cubicunits.

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Most popular questions from this chapter

find an equation that gives y as an implicit function of x. Then draw the continuous curve that satisfies this differential equation and passes through the point (2, 0).

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Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.

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