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Chapter 6: Q. 11 (page 574)

The volume of solid obtained by revolving the region between the graph f(x)=xandg(x)=x3on[0,1]around (a)the y axis (b)the line x=2

Short Answer

Expert verified

Part (a) The solid of revolution has a volume of 25蟺

Part (b) The solid of revolution has a volume of 1915蟺

Step by step solution

01

Part (a) Step 1. Given information 

We have been given to find out the volume covered by the region between the given graphs .

f(x)=xandg(x)=x3on[0,1]
02

Part (a) Step 2.Showing problem through graph 

a

03

Part (a) Step 3.

a

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Most popular questions from this chapter

The centroid of the region between the graph of f(x) = x 2

and the x-axis on [0, 2].

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

Consider the region between the graph of f(x)=3xand the x-axis on [1,3]. For each line of rotation given in Exercises 31鈥� 34, use definite integrals to find the volume of the resulting solid.

Each of the definite integrals in Exercises 19鈥�24 represents the volume of a solid of revolution obtained by rotating a region around either the x- or y-axis. Find this region.
蟺鈭�1316-x+12dx

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
See all solutions

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