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Chapter 6: Q. 10 (page 575)

The volume of the solid obtained by revolving the region between the graph of f(x)=9-x2 and the x-axis on -3,3 around (a) the x-axis and (b) the line y=鈭�3.

Short Answer

Expert verified

(a) The volume is 12965蟺cubic units.

(b) The volume is2165蟺cubic units.

Step by step solution

01

Volume around x-axis

The required region is shown below,

The volume is computed as,

V=蟺鈭�-33y2dx=蟺鈭�-33(9-x2)2dx =2蟺鈭�0381+x4-18x2dx=2蟺81x+x55-6x303=12965蟺cubicunits

02

Volume around y=-3

The outer radius of the cross-section is,

y=6-x2

The inner radius is, y=-3

The volume is computed as,

V=蟺鈭�-33(6-x2)2-(-3)2dx=2蟺鈭�0336+x4-12x2-9dx=2蟺27x+x55-4x303=2165蟺cubicunits

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Most popular questions from this chapter

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29鈥�52.

33.dydx=1-y,y0=4

Sketching disks ,washers and shells : sketch the three disks , washers , shells that result from revolving the rectangles shown in the figure around the given lines

The linex=-1

Find the exact value of the arc length of each function f(x) on [a, b] by writing the arc length as a definite integral and then solving that integral.

f(x)=1-x2,a,b=-1,1

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

dydx=ysin鈦�x

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29鈥�52

dydx=0.4y-100,y(0)=0
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