Page 215 - How To Solve Word Problems In Calculus

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3 r
x
2
= 2π r x −
3
0
3
r
3
= 2π r − − 0
3

2 3
= 2π r
3
4 3
= πr
3
8.
8 8
(x,y )
2

6 6

4 4

2 2

(x,y )
1
1 1 2 2

The x coordinate of the intersection point of the two curves is easily
calculated:

2
x = 8 − x 2
2
2x = 8
2
x = 4
x = 2

Using the washer method, the vertical rectangle shown above gen-
erates a washer of inner radius y 1 , outer radius y 2 , and thickness dx.
2
2
2
2
The volume of a typical washer is (πy − πy ) dx = π(y − y ) dx.
1
2
2
1
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