Pre-Calc Homework Solutions 305

Pre-Calc Homework Solutions 305 - Section 7.3 37. 40. 305 [...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

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.

Ask a homework question - tutors are online