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Chapter 6: Q. 26 (page 510)

Write the volume of the two solids of revolution that follow in terms of definite integrals that represent accumulations of disks and/or washers. Do not compute the integrals.

Short Answer

Expert verified

The required volume is蟺鈭�03(fx)2-12dx

Step by step solution

01

Step 1. Given Information  

The given figure is

02

Step 2. Explanation    

A solid of revolution is being formed by rotating the region around x-axis.

The given figure can be shown as below,

The part of region above x-axis is not bounded by x-axis. But it can be expressed as a washer with outer radius being the graph of the function and inner radius is the graph of y=1. The x-interval for this region is 0,4

Thus, the integral of the volume of solid formed by rotating the given region is expressed as 蟺鈭�03(fx)2-12dx

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Most popular questions from this chapter

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 .

fx=2x32+1,1,3

In the process of solving the differential equation dydx=1-yby separation of variables, we obtain the equation 鈭�ln鈦�|1鈭�y|=x+C. After solving for y, this equation becomes y=1鈭�Ae鈭�x. Given that y>1, how is A related to C?

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.

Sketching a representative disks ,washers and shells : sketch a representative disks , washers , shells for the solid obtained by revolving the regions shown in figure around the given lines .

the linex=7

Consider the region between the graph of fx=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.
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