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Using a Riemman Sum to find the area under a curve (n intervals, left endpoint)

  1. Dec 3, 2011 #1
    Hello, I'm having a bit of trouble calculating the area under the curve of x^2 on the interval x=-3 to x=1. The question says that there I have to use n subintervals and left endpoints.

    Relevant Equations

    Δx=b-a/n

    xi=a+(Δx)(i-1) -its i-1 because we're using a left endpoint, otherwise it would be just i.

    f(xi)= (a+(Δx)(i-1))^2(Δx)

    The Attempt


    Δx=b-a/n
    = 1-(-3)/n
    =4/n

    xi = -3+4/n(i-1)

    f(xi)= (-3+4/n(i-1))^2(4/n)

    =(9-(24i/n)+(24/n)+(16i^2/n^2)-(32i/n^2)-(16/n^2))*(4/n)

    I got stuck at this point. I have no idea how to move on from here. Any advice?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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