Page 214 - How To Solve Word Problems In Calculus

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4

1
= y + 1 − y 1/2 dy
0 4
4
1 2
2
= y + y − y 3/2
8 3
0
16
= 2 + 4 − − 0
3
2
=
3

7.

(x,y)

If the vertical rectangle shown is rotated about the x axis,
a disk of radius y and thickness dx is generated. The volume
2
of a typical disk is πy dx and the total volume of the solid of
revolution is

r

2
V = π y dx
We take advantage of symmetry by in-
−r
tegrating from 0 to r and doubling the
integral.

2
r
2
= 2π r − x 2 dx
0
r

2
2
= 2π (r − x ) dx
0
201