Posted in Health-01-01 by admin
on June 30, 2006
Advanced Triple
Setting up the triple integral in spherical coordinates to find the volume of a solid? Help!?
The question reads: Consider the solid region D between the spheres x^2+y^2+z^2=1 & x^2+y^2+z^2=9 and above the upper nappe of the cone z^2=3(x^2+y^2). How would you describe to solid region in spherical coordinates? And how would you set up the triple integral in spherical coordinates that can be used to find the volume V of this solid. Any help would be greatly appreciated. Thanks in advance.
The following describes the region in spherical coordinates:
The angle with respect to the z-axis, (I think it is phi, but I might have it mixed up with theta) goes from 0 to pi/6
The radius, rho, goes from 1 to 3.
The angle with respect to the x-axis (I think theta) goes from 0 to 2pi
Set up the triple integral with the limits above and you are integrating
rho^2 (sin phi) d theta d phi
 |
| 2 BOXES SCHIFF MOVE FREE ADVANCED TRIPLE STRENGTH 160 Tablets | |
 |
$22.50 (5 Bids) Time Remaining: 12h 42m |
| 2 Bottles OSTEO BI FLEX 5 Loxin Advanced Triple Strength Joint Comfort Caplets | |
 |
$17.99 Time Remaining: 14h 58m Buy It Now for only: $19.95 Buy It Now | Bid now | Add to watch list |
| 3 Aquafresh ADVANCED 2X WHITENING TRIPLE PROTECTION TOOTHPASTE ICE MINT NIB | |
 |
$9.99 Time Remaining: 20h 16m Buy It Now for only: $11.99 Buy It Now | Bid now | Add to watch list |
| Advanced Triple Boron w Calcium by Source Naturals Inc 120 Caps | |
 |
$5.86 Time Remaining: 21h 13m Buy It Now for only: $5.86 Buy It Now | Add to watch list |
| 2 Brand New 80 Count Bottles of Osteo Bi Flex Advanced Triple Strength | |
 |
$26.99 Time Remaining: 1d 1h 22m Buy It Now for only: $34.99 Buy It Now | Bid now | Add to watch list |
| Pattern Triple Arrows Purse or Wall Basket Intermediate Advanced Pattern | |
 |
$7.00 Time Remaining: 1d 13h 2m |
| 2 BOXES OF OSTEO BI FLEX WITH 5 LOXIN ADVANCED TRIPLE STRENGTH 40 TABLS | |
 |
$10.00 Time Remaining: 1d 13h 52m Buy It Now for only: $15.00 Buy It Now | Bid now | Add to watch list |
| 5 BOXES OF OSTEO BI FLEX WITH 5 LOXIN ADVANCED TRIPLE STRENGTH 200 TABS TOTAL | |
 |
$25.00 (2 Bids) Time Remaining: 1d 16h 4m |
| Sally Hansen TRIPLE STRONG Advanced Gel Fortifier Nail Polish STRENGTHENER Boxed | |
 |
$6.99 Time Remaining: 1d 17h 51m Buy It Now for only: $6.99 Buy It Now | Add to watch list |
| 2 BOXES SCHIFF MOVE FREE ADVANCED TRIPLE STRENGTH DEC 2014TTL 160 Tablets | |
 |
$29.99 Time Remaining: 1d 21h 24m Buy It Now for only: $32.99 Buy It Now | Bid now | Add to watch list |
| SCHIFF MOVE FREE ADVANCED TRIPLE STRENGTH OCT 2014TTL 160 Tablets | |
 |
$26.99 Time Remaining: 1d 21h 25m Buy It Now for only: $29.99 Buy It Now | Bid now | Add to watch list |
| 2 BOXES SCHIFF MOVE FREE ADVANCED TRIPLE STRENGTH AUG 2014TTL 160 Tablets | |
 |
$29.99 Time Remaining: 1d 21h 27m Buy It Now for only: $32.99 Buy It Now | Bid now | Add to watch list |
| Osteo Bi Flex Advanced Triple Strength 40 Coated caplet EXP 10 13 | |
 |
$3.67 Time Remaining: 1d 22h 42m Buy It Now for only: $3.67 Buy It Now | Add to watch list |
| 40 OSTEO BI FLEX 5 Loxin Advanced Triple Strength Joint Comfort Coated Caplets | |
 |
$9.95 Time Remaining: 1d 23h 36m Buy It Now for only: $10.95 Buy It Now | Bid now | Add to watch list |
| 80 OSTEO BI FLEX 5 Loxin Advanced Triple Strength Joint Comfort Caplets | |
 |
$17.95 Time Remaining: 1d 23h 37m Buy It Now for only: $19.95 Buy It Now | Bid now | Add to watch list |
| 3 Bottles OSTEO BI FLEX 5 Loxin Advanced Triple Strength Joint Comfort Caplets | |
 |
$24.95 Time Remaining: 1d 23h 37m Buy It Now for only: $27.75 Buy It Now | Bid now | Add to watch list |
| 480 OSTEO BI FLEX 5 Loxin Advanced Triple Strength Joint Comfort Coated Caplets | |
 |
$90.00 Time Remaining: 1d 23h 38m |
| NEW Skinn Crease Release Triple Advanced Eye Contour Serum Super Sized | |
 |
$24.99 (1 Bid) Time Remaining: 2d 10m |
| 144Ct Osteo Bi Flex Advanced Glucosamine Chondroitin MSM with 5 Loxin Triple | |
 |
$31.79 Time Remaining: 2d 43m Buy It Now for only: $34.99 Buy It Now | Bid now | Add to watch list |
| Schiff MOVE FREE Advanced Triple Strength 160 Tabs NIB | |
 |
$31.95 Time Remaining: 2d 1h 27m Buy It Now for only: $31.95 Buy It Now | Add to watch list |
| Osteo Bi Flex Triple Strength Tabs w D3 Glucosamine MSM w 5 Loxin Advanced 96Ct | |
 |
$29.95 Time Remaining: 2d 4h 14m Buy It Now for only: $29.95 Buy It Now | Add to watch list |
| Osteo Bi Flex Triple Strength Tabs Glucosamine MSM w 5 Loxin Advanced 40 Ct x 2 | |
 |
$15.99 Time Remaining: 2d 16h 46m Buy It Now for only: $15.99 Buy It Now | Add to watch list |
| 120 OSTEO BI FLEX ADVANCED TRIPLE STRENGTH CAPLETS Plus Bonus 30 Caplets Bottle | |
 |
$3.69 (5 Bids) Time Remaining: 2d 17h 51m |
| 3 Brand New 80 Count Bottles of Osteo Bi Flex Advanced Triple Strength | |
 |
$35.99 Time Remaining: 2d 18h 58m Buy It Now for only: $35.99 Buy It Now | Add to watch list |
| 2 Brand New 80 Count Bottles of Osteo Bi Flex Advanced Triple Strength | |
 |
$29.99 Time Remaining: 2d 18h 59m Buy It Now for only: $29.99 Buy It Now | Add to watch list |
| 2 Brand New 40 Count Bottles of Osteo Bi Flex Advanced Triple Strength | |
 |
$9.95 Time Remaining: 2d 19h 1m |
| 1 Bottle OSTEO BI FLEX 5 Loxin Advanced Triple Strength Joint Comfort Caplets | |
 |
$9.99 Time Remaining: 2d 19h 35m Buy It Now for only: $10.99 Buy It Now | Bid now | Add to watch list |
| 120 OSTEO BI FLEX 5 Loxin Advanced Triple Strength Joint Comfort Coated Caplets | |
 |
$24.99 Time Remaining: 2d 19h 36m Buy It Now for only: $27.50 Buy It Now | Bid now | Add to watch list |
| 6 Bottles OSTEO BI FLEX 5 Loxin Advanced Triple Strength Joint Comfort Caplets | |
 |
$45.00 Time Remaining: 2d 19h 37m Buy It Now for only: $49.50 Buy It Now | Bid now | Add to watch list |
| SALLY HENSEN TRIPLE STRONG ADVANCED GEL NAIL FORTIFIER | |
 |
$8.99 Time Remaining: 2d 22h 23m Buy It Now for only: $8.99 Buy It Now | Add to watch list |
| 3 Brand New 40 Count Bottles of Osteo Bi Flex Advanced Triple Strength | |
 |
$9.95 Time Remaining: 2d 23h 36m |
| 240 OSTEO BI FLEX 5 Loxin Advanced Triple Strength Joint Comfort Coated Caplets | |
 |
$44.00 Time Remaining: 2d 23h 58m Buy It Now for only: $49.00 Buy It Now | Bid now | Add to watch list |
| 12 Bottles OSTEO BI FLEX 5 Loxin Advanced Triple Strength Joint Comfort Caplets | |
 |
$87.00 Time Remaining: 3d 15h 6m Buy It Now for only: $95.70 Buy It Now | Bid now | Add to watch list |
| Skinn Dimitri James Crease Release Triple advanced Eye Contour Serum Omega 12oz | |
 |
$37.79 Time Remaining: 3d 18h 31m Buy It Now for only: $37.79 Buy It Now | Add to watch list |
| 96 Osteo Bi Flex 5 Loxin Advanced Triple Strength 96 Coated Caplets | |
 |
$25.49 Time Remaining: 3d 19h 54m Buy It Now for only: $25.49 Buy It Now | Add to watch list |
| 40 Osteo Bi Flex 5 Loxin Advanced Triple Strength 40 Coated Caplets | |
 |
$12.49 Time Remaining: 3d 19h 58m Buy It Now for only: $12.49 Buy It Now | Add to watch list |
| SCHIFF MOVE FREE ADVANCED TRIPLE STRENGTH 160 TABS | |
 |
$27.99 Time Remaining: 4d 5h Buy It Now for only: $27.99 Buy It Now | Add to watch list |
| 2 96 Ct Osteo Bi flex 5 Loxin Advanced Triple w VITAMIN D3 | |
 |
$2.75 (2 Bids) Time Remaining: 4d 20h 26m |
| 3 Brand New 80 Count Bottles of Osteo Bi Flex Advanced Triple Strength | |
 |
$35.99 Time Remaining: 5d 1h 41m Buy It Now for only: $45.99 Buy It Now | Bid now | Add to watch list |
| 160 Schiff Move Free ADVANCED Triple Strength NIB 2014 | |
 |
$29.99 Time Remaining: 5d 16h 4m Buy It Now for only: $29.99 Buy It Now | Add to watch list |
| 8 BAGS 320 DROPS HALLS ADVANCED FORMULA TRIPLE SOOTHING ACTION COUGH DROPS | |
 |
$11.99 Time Remaining: 5d 20h 42m |
| 2 osteo bi flex with 5 loxin advanced triple strength | |
 |
$14.99 Time Remaining: 5d 21h 36m |
| 3x NEUTROGENA MEN TRIPLE PROTECT FACE LOTION SPF 20 ADVANCED PROTECTION 17oz ea | |
 |
$22.99 Time Remaining: 6d 55m Buy It Now for only: $22.99 Buy It Now | Add to watch list |
| Schiff Move Free Advanced Triple Strength MSM Vitamin | |
 |
$20.89 Time Remaining: 6d 6h 40m Buy It Now for only: $20.89 Buy It Now | Add to watch list |
| Osteo Biflex Advanced Triple Strength Bottle Of 80 | |
 |
$34.92 Time Remaining: 6d 19h 47m Buy It Now for only: $34.92 Buy It Now | Add to watch list |
| Osteo Bi flex Glucosamine Chondroitin MSM with 5 loxin Advanced Triple Strength | |
 |
$10.99 Time Remaining: 6d 20h 34m |
| Advanced Graphics Triple H WWE Cardboard Stand Up 154 | |
 |
$29.95 Time Remaining: 6d 22h 31m Buy It Now for only: $29.95 Buy It Now | Add to watch list |
| SCHIFF MOVE FREE ADVANCED TRIPLE STRENGTH 140 TABS | |
 |
$27.99 Time Remaining: 7d 3h 15m Buy It Now for only: $27.99 Buy It Now | Add to watch list |
| Skinn Crease Release Triple Advanced Eye Contour Serum Omega Plus 12 oz 33 ml | |
 |
$32.95 Time Remaining: 7d 10h 22m Buy It Now for only: $32.95 Buy It Now | Add to watch list |
| Anolon Advanced Knife Block Cutlery Set 15PC Triple Riveted German Steel 52588 | |
 |
$174.99 Time Remaining: 7d 20h 57m Buy It Now for only: $174.99 Buy It Now | Add to watch list |
| SOURCE NATURALS Advanced Triple Boron capsules 120 Caps | |
 |
$9.65 Time Remaining: 7d 22h 21m Buy It Now for only: $9.65 Buy It Now | Add to watch list |
| SOURCE NATURALS Advanced Triple Boron capsules 240 Caps | |
 |
$15.65 Time Remaining: 7d 22h 21m Buy It Now for only: $15.65 Buy It Now | Add to watch list |
| Aquafresh advanced triple protection freshest ever mint | |
 |
$20.94 Time Remaining: 7d 23h 40m Buy It Now for only: $20.94 Buy It Now | Add to watch list |
| Osteo Biflex Advanced Triple Strength Bottle Of 120 | |
 |
$31.96 Time Remaining: 8d 3h 13m Buy It Now for only: $31.96 Buy It Now | Add to watch list |
| SCHIFF MOVE FREE ADVANCED TRIPLE STRENGTH 160 TABLETS | |
 |
$31.90 Time Remaining: 8d 11h 8m Buy It Now for only: $31.90 Buy It Now | Add to watch list |
| SCHIFF Move Free Advanced Triple Strength Vitamin Joint Arthritis schiff new | |
 |
$27.99 Time Remaining: 8d 16h 46m Buy It Now for only: $27.99 Buy It Now | Add to watch list |
| Schiff Move Free Advanced Triple Strength 160 Tablets | |
 |
$27.89 Time Remaining: 9d Buy It Now for only: $27.89 Buy It Now | Add to watch list |
| 2 Osteo Bi Flex TRIPLE STRENGTH 5 Loxin Advanced Joint Comfort 80 Caplets Total | |
 |
$13.99 Time Remaining: 9d 12h 56m Buy It Now for only: $13.99 Buy It Now | Add to watch list |
| 384Ct Osteo Bi Flex Biflex Triple 3X Strength Advanced Joints Arthritis 20 More | |
 |
$49.95 Time Remaining: 9d 15h 18m Buy It Now for only: $49.95 Buy It Now | Add to watch list |
| Schiff Move Free Advanced Triple Strength 160 Tablets | |
 |
$22.99 Time Remaining: 10d 1h 2m Buy It Now for only: $22.99 Buy It Now | Add to watch list |
| Move Free Advanced Supplement Triple Strength 160 Tablets | |
 |
$36.85 Time Remaining: 10d 14h 32m Buy It Now for only: $36.85 Buy It Now | Add to watch list |
| Osteo Biflex Advanced Triple Strength Bottle Of 40 | |
 |
$17.37 Time Remaining: 10d 21h 57m Buy It Now for only: $17.37 Buy It Now | Add to watch list |
| Schiff Move Free Advanced Triple Strength Joint Care 40 Coated Tablets | |
 |
$21.99 Time Remaining: 11d 20h 37m Buy It Now for only: $21.99 Buy It Now | Add to watch list |
| Schiff Move Free Advanced Triple Strength Tablets 80 ea | |
 |
$26.99 Time Remaining: 12d 20h 9m Buy It Now for only: $26.99 Buy It Now | Add to watch list |
| Aquafresh Advanced triple protection toothpaste 180 tubes 08oz NEW IN BOX | |
 |
$110.00 Time Remaining: 12d 23h 35m Buy It Now for only: $110.00 Buy It Now | Add to watch list |
| Move Free Advanced Triple Strength Glucosamine 160 ct | |
 |
$38.99 Time Remaining: 13d 1h 52m Buy It Now for only: $38.99 Buy It Now | Add to watch list |
| 2 BOXES SCHIFF MOVE FREE ADVANCED TRIPLE STRENGTH 04 2014 160 Tablets | |
 |
$32.95 Time Remaining: 14d 1h 8m Buy It Now for only: $32.95 Buy It Now | Add to watch list |
| Osteo Bi Flex Advanced Triple Strength Joint Shield w 5 Loxin 80 Caplets | |
 |
$15.99 Time Remaining: 14d 16h 2m Buy It Now for only: $15.99 Buy It Now | Add to watch list |
| Osteo Bi Flex Advanced Triple Strength Joint Shield w 5 Loxin 144 Caplets | |
 |
$22.99 Time Remaining: 14d 16h 10m Buy It Now for only: $22.99 Buy It Now | Add to watch list |
| LOT OF 5 Schiff Move Free Advanced Triple Strength 5 x 160 800 Tablets | |
 |
$159.99 Time Remaining: 14d 17h 11m Buy It Now for only: $159.99 Buy It Now | Add to watch list |
| Source Naturals Advanced Triple Boron with Calcium | |
 |
$13.37 Time Remaining: 14d 17h 23m Buy It Now for only: $13.37 Buy It Now | Add to watch list |
| 3 RESOLVE Carpet Stain Remover Formerly SPRAY N WASH Triple OXI Advanced | |
 |
$11.99 Time Remaining: 14d 18h 37m Buy It Now for only: $11.99 Buy It Now | Add to watch list |
| Schiff Move Free Advanced Triple Strength 160 Tablets | |
 |
$26.99 Time Remaining: 15d 11h 23m Buy It Now for only: $26.99 Buy It Now | Add to watch list |
| Aquafresh Advanced triple protection toothpaste 8 tubes | |
 |
$5.25 Time Remaining: 15d 12h 33m Buy It Now for only: $5.25 Buy It Now | Add to watch list |
| COSMEDICINE TRIPLE P SERUM DAILY ADVANCED CARE 1 fl oz | |
 |
$59.95 Time Remaining: 15d 15h 31m Buy It Now for only: $59.95 Buy It Now | Add to watch list |
| Sally Hansen Triple Strong Advanced Gel Nail Fortifier 2620 Clear | |
 |
$4.99 Time Remaining: 15d 15h 51m Buy It Now for only: $4.99 Buy It Now | Add to watch list |
| 140 Coated Tablets Move Free Advanced Triple Strength | |
 |
$37.85 Time Remaining: 16d 1h 50m Buy It Now for only: $37.85 Buy It Now | Add to watch list |
| Schiff Move Free Advanced Triple Strength 80 coated Tablets Expiration 12 2014 | |
 |
$21.99 Time Remaining: 16d 3h 49m Buy It Now for only: $21.99 Buy It Now | Add to watch list |
| Schiff Move Free 160 Advanced Triple Strength MoveFree Advance Glucosamine Plus | |
 |
$29.48 Time Remaining: 16d 7h 47m Buy It Now for only: $29.48 Buy It Now | Add to watch list |
| Schiff Move Free Advanced Triple Strength 160 Tablets | |
 |
$37.90 Time Remaining: 16d 14h 31m Buy It Now for only: $37.90 Buy It Now | Add to watch list |
| 1 BX SCHIFF MOVE FREE ADVANCED TRIPLE STRENGTH | |
 |
$27.99 Time Remaining: 16d 20h 7m Buy It Now for only: $27.99 Buy It Now | Add to watch list |
| 1 40ct Osteo Bi Flex w 5 Loxin Advanced Triple Strength EXP 2014 | |
 |
$4.25 Time Remaining: 16d 23h 44m Buy It Now for only: $4.25 Buy It Now | Add to watch list |
| 2 40ct Osteo Bi Flex w 5 Loxin Advanced Triple Strength EXP 2014 | |
 |
$8.00 Time Remaining: 16d 23h 50m Buy It Now for only: $8.00 Buy It Now | Add to watch list |
| 4 40ct Osteo Bi Flex w 5 Loxin Advanced Triple Strength EXP 2014 | |
 |
$14.99 Time Remaining: 17d 7m Buy It Now for only: $14.99 Buy It Now | Add to watch list |
| Schiff Move Free Advanced Triple Strength Glucosamine Plus 160ct | |
 |
$30.45 Time Remaining: 17d 15h 44m Buy It Now for only: $30.45 Buy It Now | Add to watch list |
| Osteo Bi Flex Triple Strength With 5 Loxin Advanced One x 80 | |
 |
$19.99 Time Remaining: 17d 19h 38m Buy It Now for only: $19.99 Buy It Now | Add to watch list |
| Osteo Bi Flex Triple Strength with 5 LOXIN Advanced 2 Per Day 40 Coated Caplets | |
 |
$7.50 Time Remaining: 17d 19h 46m Buy It Now for only: $7.50 Buy It Now | Add to watch list |
| OSTEO BI FLEX 5 LOXIN ADVANCED TRIPLE STRENGTH w VIT D3 2000 IU 80 CAPLETS | |
 |
$11.99 Time Remaining: 17d 23h 48m Buy It Now for only: $11.99 Buy It Now | Add to watch list |
| OSTEO BI FLEX JOINT SHIELD ADVANCED TRIPLE STRENGTH w VIT D + MSM 80 CAPLETS | |
 |
$10.99 Time Remaining: 17d 23h 54m Buy It Now for only: $10.99 Buy It Now | Add to watch list |
| ED HARDY HOLLYWOOD BRONZE ADVANCED TRIPLE PACK FREE SHIPPING FREE GIFT | |
 |
$46.99 Time Remaining: 18d 22h 9m Buy It Now for only: $46.99 Buy It Now | Add to watch list |