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Chapter 6: Q. 9 (page 574)

Finding geometric quantities with definite integrals: Set up and solve definite integrals to find each volume, surface area, or arc length that follows. Solve each volume problem both with disks/washers and with shells, if possible.

The volume of the solid obtained by revolving the region between the graph of f(x)=x2and the y-axis for 0鈮�x鈮�2around (a) the x-axis and (b) they-axis .

Short Answer

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Step by step solution

01

Step 1. Given Information.

The volume of the solid obtained by revolving the region between the graph of f(x)=x2and the y-axis for0鈮�x鈮�2.

02

(a) Step 2. Calculation.

The volume is given by :

V=2蟺鈭�abyg(y)dy

As y=x2

V=2蟺鈭�abyfxdyV=2蟺鈭�02y路y2dyV=2蟺鈭�02y3dyV=2蟺y4402V=2蟺4脳4V=2蟺

03

(b) Step 3. Around the y-axis.

The volume of solid revolving about the y-axis is

role="math" localid="1652262266017" V=2蟺鈭�abxfxdxV=2蟺鈭�02x路x2dxV=2蟺鈭�02x3dxV=2蟺x4402V=2蟺4脳16V=8蟺

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Most popular questions from this chapter

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

The area of the surface obtained by revolving the curve

fx=sin蟺xaround the x-axis on-1,1.

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

dydx=xe鈭�y

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

dydx=-2y(1-3y),y(0)=2

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

dydx=3y(1-y),y(0)=1
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