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Chapter 6: Q. 43 (page 511)

Consider the region between the graph of fx=4-x2and the liney=5on 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 is16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�043-4-y-12dyV1=蟺鈭�0412-y-64-ydyV1=蟺12y-y22-64-y32-3204=V1=蟺12y-y22+44-y3204V1=蟺48-8+40-32=8蟺

and

V2=蟺鈭�459-1dy=8蟺鈭�45dyV2=8蟺5-4=8蟺

Now,

V=V1+V2V=8蟺+8蟺=16蟺

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Most popular questions from this chapter

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