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Chapter 6: Q. 9 (page 575)

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) the y-axis

Short Answer

Expert verified

(a) The volume of solid about x- axis is 325蟺cubic units.

(b) The volume of solid about y-axis is 8蟺cubic units.

Step by step solution

01

Volume around x-axis.

The graph of f(x)=x2,0鈮�x鈮�2is shown below,

The volume is computed as,

V=鈭�ab蟺测2dx=蟺鈭�02x22dx=蟺鈭�02x4dx=蟺x5502=325蟺cubicunits

02

Volume around the y- axis.

The volume is computed as,

V=鈭�ab蟺虫2dy=蟺鈭�04ydy=蟺y2204=162蟺=8蟺cubicunits

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Most popular questions from this chapter

Consider the region between the graph of f(x)=x-2and the x-axis on [2,5]. For each line of rotation given in Exercises 35鈥� 40, use definite integrals to find the volume of the resulting solid.

Approximate the arc length of f (x) on [a, b], using n line segments and the distance formula. Include a sketch of f (x) and the line segments .

fx=x3,a,b=-2,2,n=4

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

dydx=x+1x

Consider the region between f(x)=xand the x-axis on [0,4]. For each line of rotation given in Exercises 27鈥�30, use four disks or washers based on the given rectangles to approximate the volume of the resulting solid.

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