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Thread: Find the area by taking the limit

  1. #1
    Feb 2009

    Find the area by taking the limit


    the graph is f(x) = x

    between x = 0 and x = 1

    n= 6 from the diagram

    using the right reiman sum

    1/6 ( f(1/6)+f(2/6)+f(3/6)+f(4/6)+f(5/6)+f(6/6)) = 1/6 (21/6) = 7/12

    but the limit part confuses me

    lim sum n i=1 (i/n2)(1/n) = sum n i=1 i^2/n^3
    n-> infinity

    1/n^3 sum n i=1 i^2 but then I don't know what I am suppose to do

    I am following an example in my text and all of a sudden it becomes ns and I don't know what happened to "i"

    Any enlightenment on what I am doing is greatly appreciated.


    this calculus beginner - the term is almost over and I still feel very much like a beginner....thanks for all of you experts who help us.
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  2. #2
    MHF Contributor matheagle's Avatar
    Feb 2009
    The area, since it's a triangle from (0,0) to (1,1), is .5.
    I don't know where you're getting that Reimann sum from.
    But that limit is 1/3.
    Explain your sum.
    I think you are integrating $\displaystyle x^2$ instead from (0,0) to (1,1), which has area 1/3.
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