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Chapter 6: Q. 50 (page 523)

Use definite integrals to find the volume of each solid of revolution described in Exercises 49鈥�61. (It is your choice whether to use disks/washers or shells in these exercises.)

The region between the graph of f(x)=e2xand the x-axis on [0, 4], revolved around the x-axis.

Short Answer

Expert verified

The integral does not exist

Step by step solution

01

Given information

We are given a functione2x

02

FInd the integral and evaluate it

We know that the integral can be given as

V=2蟺鈭�cdr(y)h(y)dy. The axis of revolution is x-axis hence the radius is r(y)=yand the height can be given as h(y)=12lnyand substituting the value in the integral we get,

V=蟺鈭�04y(lny)dyV=蟺[y22lny-y24]40 integraldoesnotexist

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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.

30.dydx=3x,y0=4

Solve the initial-value problem

dydx=2y1-5y,y0=1

The arc length of the curve is traced out by the graph of f(x)=ln(csxx)on the interval 蟺4,蟺2.

We have been given

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals

蟺鈭�0蟺2cos2xdxand蟺鈭�蟺2蟺cos2xdx
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