August 26th, 2008, 01:27 PM  #1 
Newbie Joined: Aug 2008 Posts: 1 Thanks: 0  Volume
Hi, Let the volume D be: x >= 0 y >= 0 x²+y²<= 1 0<= z <= (x²y²)/2 Compute the volum of D. Thx J. 
August 27th, 2008, 01:18 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,822 Thanks: 723  Re: Volume Quote:
Step 1: z integral = (x^2y^2)/2 Step 2: set up the x,y integral. It will be a subset of the plane bounded by the x axis, the line y=x and the arc of the unit circle from the x axis to the y=x line. The figure looks like a pizza slice, 1/8 of a pie. Step 3: convert the integral to polar coordinates. Then the domain of integral is r from 0 to 1 and t (angle) from 0 to pi/4. I got an answer of 1/16.  

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