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Chapter 6: Q. 42 (page 511)

Consider the region between the graph of fx=4-x2and the line y=5on 0,2. For each line of rotation given in Exercises 41鈥�44, use definite integrals to find the volume of the resulting solid.

Short Answer

Expert verified

The volume of the solid is203蟺

Step by step solution

01

Step 1. Given Information

The given figure is

fx=4-x2=yx=4-y=gy

02

Step 2. Finding Volume

V1=蟺鈭�042-4-y2dy=蟺鈭�048-y-44-ydy

V1=蟺8y-y22+834-y3204V1=蟺32-8+0-643=蟺24-643=83蟺

localid="1649521140016" V2=蟺鈭�454dy=4蟺鈭�451dy=4蟺5-4=4蟺

Now, V=V1+V2

V=83蟺+4蟺=203蟺

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