Pre-Calc Homework Solutions 306

Pre-Calc Homework Solutions 306 - 306 Section 7.3 45. 8 5...

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: 306 Section 7.3 45. 8 5 43. continued (c) A shell has radius 1 y. The volume is y 3) dy [ 1, 3] by [ 1.4, 9.1] 2 0 8 5 1 0 y 12( y 2 y4 24 24 1 5 y 5 13 3 8 2 y y dy 5 5 1 13 4 8 3 y y 2 . 20 15 0 2 . The volume is 5 The functions intersect at (2, 8). (a) Use washer cross sections: a washer has inner radius r A(x) 2 0 (d) A shell has radius y 1 x 3, outer radius R (R 2 4x, and area (16x 2 16 3 x 3 2 0 y 1 24 0 24 2 12( y 2 y 3) dy 5 2 2 3 3 y4 y y dx 5 5 1 1 5 3 4 2 3 y y y 2 . 5 20 15 0 y4 4 r ) x 6) dx 2 x 6). The volume is 1 7 x 7 2 0 (16x 2 512 . 21 (b) Use cylindrical shells: a shell has a radius 8 height y 1/3 y . The volume is 4 8 y 2 (8 y) y 1/3 dy 4 0 8 y2 2 8y 1/3 2y y 4/3 dy 4 0 8 3 7/3 832 1 3 2 6y 4/3 y 2 y y . 7 21 12 0 y and y2 44. A shell has height 2 y2 y4 y2 . 2 4 (a) A shell has radius y. The volume is 2 0 2 (y) y 2 y4 dy 4 2 1 4 y 4 1 6 y 24 2 0 8 . 3 46. (b) A shell has radius 2 2 y. The volume is 4 2 (2 0 2 y) y 2 y5 4 y 4 dy [ 0.5, 1.5] by [ 0.5, 1.5] 2 0 2 1 6 y 24 y4 y 3 2y 2 dy 2 1 4 2 3 1 5 y y y 4 3 10 The functions intersect at (0, 0) and (1, 1). 2 0 8 . 5 (a) Use cylindrical shells: a shell has radius x and height 2x x2 x x x 2) dx x 2. The volume is 2 1 3 x 3 1 4 x 4 1 0 (c) A shell has radius 5 2 y. The volume is 1 2 (5 0 2 y) y 2 y5 4 5y 4 4 1 5 y 4 y4 dy 4 2 (x)(x 0 6 . x and 2 0 y3 1 4 y 4 5y 2 dy 5 3 y 3 2 (b) Use cylindrical shells: a shell has radius 1 height 2x 8 . 1 2 1 6 y 24 x 2 x x x . The volume is 1 2 0 0 2 (1 x)(x x 2) dx 2 0 (x 3 2x 2 2 3 x 3 x) dx 1 2 x 2 1 0 (d) A shell has radius y 2 5 . The volume is 8 y 4 4 2 6 1 4 x 4 2 0 y 2 5 8 y5 4 1 6 y 24 y2 5y 4 32 . dy y3 1 4 y 4 5y 2 dy 8 5 3 y 24 2 2 0 2 1 5 y 32 4 . 0 ...
View Full Document

Ask a homework question - tutors are online