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Chapter 6: Q. 35 (page 511)

Consider the region between the graph of f(x)=x-2 and 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 is36蟺

Step by step solution

01

Step 1. Given Information     

The given figure is

02

Step 2. Calculation      

Express the curve as inverse function.

y=x-2x=y+2g(y)=y+2

For the x-interval of [2,5], the corresponding interval of y-variable will be [0,3]

For the washer the external radius of each washer isx=5and internal radius of each wahser is given byg(y)

03

Step 3. Calculation

Determine the volume of solid of revolution.

V=蟺鈭�0352-g(y)2dx=蟺鈭�0325-y+22dy=蟺鈭�0325-y2-4y-4dy=蟺鈭�0321-y2-4ydy=蟺21y-y33-4y2203dy=蟺21(3)-333-4(3)22-21(0)-033-4(0)22=蟺63-9-18-0=36蟺

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Most popular questions from this chapter

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.

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