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Resolving an Integral by Upper and Lower Sums

  1. Feb 3, 2013 #1
    So, the problem statement says that i have to determinate the Upper and Lower Sums that aproximate the area under the graph given by the next function: [tex]f(x) = x^3[/tex] in the interval[0,1] with a partition of 0,2

    So, i preoceeded to determinate the Upper and Lower Sums but I dont come up with the righ answer (i know because i corroborated by getting the resault of the integral [itex]\int x^3\, dx[/itex] betwen 0 and 1, with my calculator)

    P={0; 0,2; 0,4; 0,6; 0,8;1}
    [itex]L(f,P) = \sum^{5}_{i=0}[/itex]mi(ti-ti-1) = [itex](0^3)(0,2) + (0,2^3)(0,2) + (0,4^3)(0,2) + (0,6^3)(0,2) + (0,8^3)(0,2) = 0,10[/itex]


    That is just plain wrong but i dont know what im doing wrong...well i wont redact how i did the Upper sums because i guess you got the point...

    Thanks.
     
    Last edited: Feb 3, 2013
  2. jcsd
  3. Feb 3, 2013 #2

    SammyS

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    I get 0.016 --- or as you write it, 0,016 .
     
  4. Feb 3, 2013 #3
    Yes, sorry I posted the answer wrong, its 0.16, but what concerns me is that if i did it ok or is wrong the preocedure...
     
  5. Feb 3, 2013 #4

    SammyS

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    The procedure is correct. (Lower sum)
     
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