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Solid that lies above the square (in the xy-plane)

  1. Oct 17, 2005 #1
    Consider the solid that lies above the square (in the xy-plane) R= [0,1] X [01]
    and below the elliptic paraboloid z= 64 -x^2 +4xy -4y^2

    Estimate the volume by dividing R into 9 equal squares and choosing the sample points to lie in the midpoints of each square.

    i'm not sure how you would dividing R into equal squares, cause it's an odd number. can someone help me get this started
  2. jcsd
  3. Oct 17, 2005 #2


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    That would be a 3X3 array of squares which is reasonable considering that the paraboloid is off-center with respect to the square. Obviously, if you divided the original square into a much larger number of areas you would get more accuracy at the expense of doing a lot more work. Fewer squares mean less work but also reduced accuracy. 9 seems like a good optimum!
  4. Oct 17, 2005 #3
    i dont know what i was thinking, thank you
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