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Chapter 6: Q. 37 (page 511)

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.

Short Answer

Expert verified

The required volume is18蟺

Step by step solution

01

Step 1. Given Information   

The given figure is

02

Step 2. Calculation      

The external radius of each washer is 3 and internal radius of each washer is given as 3-f(x)

Determine the volume of solid of revolution.

localid="1649179581249" V=蟺鈭�2532-(3-f(x))2dx=蟺鈭�2532-(3-(x-2))2dx=蟺鈭�259-(3-x+2)2dx=蟺鈭�259-(5-x)2dx=蟺鈭�259-25+10x-x2dx=蟺-16x+10x22-x3325=蟺-16(5)+10522-533--16(2)+10222-233=18蟺

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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

dydx=-21-3y,y(0)=2

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

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.

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

蟺鈭�01e2xdxand蟺鈭�01(e2x-1)dx

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
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