math192_hw8sp06 - HW8 Solutions 15.3: Double Integrals in...

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: HW8 Solutions 15.3: Double Integrals in Polar Form 1 0 - 0 - 10. -1 2 1-y 2 4 x2 + y 2 dxdy = 1 + x2 + y 2 xy 2 dxdy = rdrd = 3/2 /2 0 2 sin 1 4r2 drd = 4 1 + r2 3/2 /2 0 1 1- 1 1 + r2 drd = 4 - 2 14. 0 1-(y-1)2 /2 1+cos 1 1-cos 1 /2 0 0 a /2 0 /2 0 4 sin2 cos r4 drd = - 5 8+ 4 18. A = 2 0 3/2 (2 cos + cos2 )d = 26. I0 = /2 rdrd = 2 + r 4 4 3a2 /2 0 4 29. average = a2 a2 - r2 drd = a3 d = 2a 3 15.4: Triple Integrals in Rectangular Coordinates 2 3 0 0 4-x2 2 3 0 2 4. = 3 x 2 3 0 2 0 0 1 0 3 2 0 dzdydx = 4 - x2 + 4 sin-1 0 0 3-3x 0 1 1-x2 0 2 2 3 0 4-x2 -y 3-3x-y 4-x2 x 2 2 0 2 0 4 - x2 dydx = 0 3 4 - x2 dx = 6 sin-1 1 = 3 0 4-x2 3 2 4-z 2 0 0 3 dzdxdy, 0 4-z 2 3 2 0 0 0 4-z 2 dydzdx, 0 dydxdz, dxdydz, 0 dxdzdy dzdydx = 3 2 1 1-x2 0 0 1 0 10. 0 16. 1 0 0 xdzdydx = x(1 - x2 - y)dydx 1 x (1 - x ) - (1 - x2 ) dx = 2 1 1 x(1 - x2 )2 dx = - (1 - x2 )3 2 12 1 = 0 1 12 22. 1 1 0 1 (a) 0 - z dydzdx dydxdz dxdydz (b) 0 1 -1 1 - z (c) 0 0 -1 - z 1 -1 0 1 0 - 1-x2 4-x2 0 26. V = 2 0 2 -y 0 3-x 1 0 - 1-x2 1 dzdydx = -2 dzdydx = 12 ydydx = 0 0 (1 - x2 )dx = 2 3 32. V = 2 -2 - 4-x2 2 4-x x 0 44. 4 0 = 0 sin 2z 4-z 2 4-x x sin 2z sin 2z dydzdx = dzdx = 4-z 4-z 0 0 0 4 1 1 1 1 (4 - z)dz = - cos 2z = - + sin2 z 2 4 4 2 0 2 4 0 4 0 4-z = 0 sin2 4 2 sin 2z 4-z xdxdz ...
View Full Document

This homework help was uploaded on 02/05/2008 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).

Ask a homework question - tutors are online