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Double Riemann Sums: Basic Problem

  1. Oct 29, 2012 #1
    1. The problem statement, all variables and given/known data
    If R = [0,4]x[-1,2], use a Riemann sum with m=2, n=3 to estimate the value of ∫∫(1-xy^2)dA. Take the sample points to be the lower right corners.


    2. Relevant equations
    None


    3. The attempt at a solution
    2*1[f(2,-1) + f(2,0) + f(2,1) + f(4,-1) + f(4,0) + f(4,1)] = some value

    Just wondering if the setup is correct, particularly the 2 and the 1 at the beginning.

    Edit:

    Would the solution for the upper left corners of the rectangles be

    2*1[f(0,-1)+ f(0,0)+ f(0,1) +f(2,-1) + f(2,0) + f(2,1)]
     
    Last edited: Oct 29, 2012
  2. jcsd
  3. Oct 29, 2012 #2

    LCKurtz

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    Yes, that looks OK

    (0,-1) isn't the upper left corner of any rectangle. Did you accidentally do lower left?
     
  4. Oct 29, 2012 #3
    Yes, I think I did do lower left. I changed it and it came out to -8. Sounds close enough to me haha. Thanks a bunch for your help.
     
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