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Chapter 6: Q. 60 (page 524)

The area centered on the line x=-1between the graph of f(x)=x2+2and the x-axis on [1,3].

Short Answer

Expert verified

The volume of the solid of revolution is 2483蟺.

Step by step solution

01

Given information

Consider the given function,

f(x)=x2+2f(x)=x2+2

02

Calculation.

The region is enclosed by the expression f(x)=x2+2and the x-axis on [-1,3].

Use the shell method with shells on the x-axis having radius x-(-1)=x+1, where x ranges from localid="1661340316266" -1to3, and height f(x)=x2+2, as the region is revolved around the line x=-1.

Thus, the volume is provided by

localid="1661340332870" Volume=2蟺鈭�-13(x+1)x2+2dx=2蟺鈭�-13x3+x2+2x+1dx=2蟺x44+x33+x2+x-13=2蟺814+9+9+3-14-13+1-1

Therefore the volume of the solid of revolution is localid="1661340343180" 2483蟺.

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