homework help > math > calculus q&a board > topic: integration in polar coordinates...

Q BgQuestion:

      
Pupil
Karma Points: 75
Respect (100%):
posted by  dsfflk on 9/3/2009 6:52:13 PM  |  status: Closed  |  Earned Karma: 75

Integration in polar coordinates

Course Textbook Chapter Problem Needs by
N/A Multivariable Calculus Early Transcendentals, Jon Rogawski 15.4 8 9/4/2009 at 9:00:00 AM
Question Details:
Let W be the region above the sphere and below the paraboloid .
Compute the volume of W using polar coordinates.
Tags: Calculus
Bonus Point Alert! Earn +8 additional karma points for helping this platinum member.

AAnswers:

Answer Question Ask for clarification
Oracle
Karma Points: 30,644
posted by Kingle on 9/3/2009 7:23:03 PM  |  status: Live
Asker's Rating: Lifesaver   
Response Details:
   ===> 
 and      ===>    ===>   
so we have
     ====>      ===>    ====>  and
so the two objects, the paraboloid and the sphere intersect form z = -1 to z = 2
so we have the triple integral
now, when z = 0 is the xy-plane so we have that   for the paraboloid and   for the sphere
so the radius is going from    remember that
also the angle θ varies as follows   
using cylindrical cordinates we have
   the integration is straight forward from there.
Hope this helps
Answer Question Ask for clarificarion
Ask New Question

Join Cramster's Community

Cramster.com brings together students, educators and subject enthusiasts in an online study community. With around-the-clock expert help and a community of over 100,000 knowledgeable members, you can find the help you need, whenever you need it. Join for free today » How Cramster is different from tutoring »

Need Help In

Useful Links