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Oracle
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posted by  booboo123 on 7/24/2008 11:03:07 PM  |  status: Live  

calc 3

Course Textbook Chapter Problem
Calculus N/A N/A N/A
Question Details:
Evaluate the paraboloid  z = 53 - 2x2 - 2y2  bounded by the plane z = 3.  Convert to polar coordinates before integrating.
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Sage
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posted by stejaes on 8/12/2008 5:06:37 AM  |  status: Live
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booboo123's comment:
"thanks a ton stejaes!"
Response Details:
Use cylindrical coordinates. The Jacobian is r. So the volume is
 
=1526.28901.
Tags: Math, Calculus
(Cramster SME)
posted by rowthu on 8/12/2008 5:40:20 AM  |  status: Live
Asker's Rating: Helpful   
booboo123's comment:
"wow, thx very much row!"
Response Details:
From the figure ,the circle at z=3 is drawn by taking z=3 in the equation og given paraboloid.
To find the volume above the plane and inside the paraboloid ,we take the circle at z=3 as the region of integration.
Hence the volume is given by,
 
Feel free to message me with your doubt before rating my answer.  :)
Tags: Math, Calculus
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