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Unformatted text preview: Section 7.3
37. 40. 305 [ 2, 2] by [ 1, 2] [ 2, 2] by [ 1, 3] The curves intersect at ( 1, 1). (a) A cross section has radius r A(x) r2 (1 x 2)2 1 (1 x and area 2x 2 x 4). 41.
1 x2
2 2 x x at x 1. A shell has radius x and height
1 0 2
1 0 x 2. The volume is x x 2) dx 2 x2
1 3 x 3 1 4 x 4 5 . 6 2 (x)(2
16 . 15 The volume is
1 (1
1 2x 2 x 4) dx x 2 3 x 3 1 5 x 5 1 (b) Use cylindrical shells: a shell has radius 2 height 2 y. The volume is
1 1 y and
[ 1, 5] by [ 1, 3] 2 (2
0 y)(2 y) dy 4
0 (2
4 3/2 y 3 y y 3/2) dy
2 5/2 y 5
1 0 A shell has radius x and height
56 . 15
4 x. The volume is
128 . 5 4 2 (x)(
0 x) dx 2 2 5/2 x 5 4 0 42. (c) Use cylindrical shells: a shell has radius y height 2 y. The volume is
1 1 1 and 2 (y
0 1)(2 y) dy 4
0 ( y3/2 y) dy
2 3/2 y 3
1 0 [ 2, 2] by [ 2, 2] 4 38. (a) A cross section has radius r A(x)
b 0 2 5/2 y 5 64 . 15 The functions intersect where 2x A shell has radius x and height x
1 0 1 x, i.e., at x 1. h 1 x and area b r2
2 h2 1
x 2 dx b h 1 x 2 . The volume is b b b x 3 h2 1 bh 2. 3 3 b 0 (2x x 1) 2x x 2x 2 1. The volume is
1 2 (x)( 1) dx (x 3/2 2x 2
2 3 x 3 x) dx
1 2 x 2
1 0 0 2
7 . 15 2 5/2 x 5 (b) Use cylindrical shells: a shell has radius x and height h 1
x . The volume is b b x 2 (x)h 1 dx 2 h b 0 43. A shell has height 12(y 2
b y 3). x
0 2 h x2 39. 1 2 x2 dx b b x3 b 2h. 3 3b 0 (a) A shell has radius y. The volume is
1 0 2 (y)12(y 2 y 3) dy 1 24
0 ( y3 y 4) dy
1 5 y 5
1 0 24 (b) A shell has radius 1
1 1 4 y 4 6 . 5 y. The volume is y 3) dy y 2) dy
1 3 y 3
1 0 2 (1
0 1 y)12(y 2 ( y4 2y 3
1 4 y 2
0 24
[ 2, 3] by [ 2, 3] 24 A shell has radius x and height x
2 x 2 3 x. 2 1 5 y 5 4 . 5 The volume is
0 2 (x) x dx 3 2 x3 2 8 .
0 ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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