Unformatted text preview: Section 7.3
23. 26. 303 [ 2, 3] by [ 1, 6] [ 1, 5] by [ 3, 1] The curves intersect when x 2 1 x 3, which is when x 2 x 2 (x 2)(x 1) 0, i.e., when x 1 or x 2. Use washer cross sections: a washer has inner radius r x 2 1, outer radius R x 3, and area A(x) (R 2 r 2) [(x 3)2 (x2 1)2] ( x 4 x 2 6x 8). The volume is
2 1 The curves intersect where x 2, which is where x 4. Use washer cross sections: a washer has inner radius r x, outer radius R 2, and area A(x) (R 2 r 2) (4 x).
4 The volume is
0 (4 x) dx 4x 1 2 x 2 4 8
0 27. ( x4
1 5 x 5 32 5 x2
1 3 x 3 8 3 6x 8) dx
2 3x 2 12 16 8x
1 1 5 1 3 3 8 117 . 5 [ 0.5, 1.5] by [ 0.5, 2] 24. The curves intersect at x radius r A(x)
0.7854 0.7854. A cross section has 2 r2 ( 2 ( sec x tan x and area 2 sec x tan x)2. Use NINT to find 2.301. [ 2, 3] by [ 1, 5] sec x tan x)2 dx 0 The curves intersect when 4 x 2 x, which is when x2 x 2 (x 2)(x 1) = 0, i.e., when x 1 or x 2. Use washer cross sections: a washer has inner radius r 2 x, outer radius R 4 x 2, and area A(x) (R 2 r 2) [(4 x 2)2 (2 x)2] (12 4x 9x 2 x 4). The volume is
2 2 28. [ 1, 3] by [ 1, 3] The curve and horizontal line intersect at x 9x 2 3x 3 24
32 5 2 . A cross (12
1 4x 2x 2 8 x 4) dx
1 5 x 5
2 section has radius 2 A(x) r2 4 (1 2 sin x and area sin x)2 4 (1 2 sin x sin2 x). 12x 24 25. The volume is
1
/2 12 2 3 1 5 108 . 5 4 (1
0 2 sin x 2 cos x 2 (3 sin2 x) dx
1 sin 2x 4
/2 0 4 4 29.
3 3 x 2 3 4 8) , 3 by [ 0.5, 2] Use washer cross sections: a washer has inner radius r sec x, outer radius R 2, and area A(x) (R 2 r 2) (2 sec2 x). The volume is
/4 [ 1, 3] by [ 1.5, 1.5] A cross section has radius r
/4 5y 2 and area
1 (2
/4 sec2 x) dx 2x tan x
/4 A(y) r2 5 y 4.
1 The volume is 1 5 y 4 dy y5 2 .
1 2
2 1 2 . 1 2 ...
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 Spring '08
 GERMAN
 Interior, Classless InterDomain Routing, washer cross sections

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