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Math Help - Left end points

  1. #1
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    Left end points

    Consider the given function.
    Evaluate the Riemann sum for 2 ≤ x ≤ 14, with six subintervals, taking the sample points to be left endpoints.

    Part 1 of 3

    We must calculate L6 =
    6 f(xi−1) Δx = [f(x0) + f(x1) + f(x2) + f(x3) + f(x4) + f(x5)] Δx,where x0, x1, x2, x3, x4, x5 represent the left hand endpoints of six equal sub-intervals of [2, 14]
    i=1




    Since we wish to estimate the area over the interval [2, 14]
    using 6 rectangles of equal widths, then each rectangle will have width Δx=2



    We wish to find L6 = (2)[ f(x0) + f(x1) + f(x2) + f(x3) + f(x4) + f(x5)].
    Since x0, x1, x2, x3, x4, x5
    represent the left-hand endpoints of the six sub-intervals of [2, 14],
    then we must have the following.

    ================================================== ================================================== ===========

    I know that delta x= 14-2/6 which is 2. I'm not sure how to get these values:

    x0,x1,x2,x3,x4,x5. Do I have to make the graph?

    I appreciate any advice or insight!!









    Last edited by Steelers72; February 8th 2013 at 08:50 PM.
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  2. #2
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    Re: Left end points

    Hey Steelers72.

    Hint: x0 = 2, x1 = 2 + deltax = 4, x2 = 2 + 2*deltax = 6, and so on.... (Now just evaluate the functions at these points)
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  3. #3
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    Re: Left end points

    Thanks ! If you don't mind, how exactly did you get the values? Like, which formula or equation did you start to plug numbers in?
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  4. #4
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    Re: Left end points

    Your questions asks for equal-sub intervals which means the space between them is constant and happens to be the delta x value.
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  5. #5
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    Re: Left end points

    OH now I remember when did this in lecture. when they dont give you a graph you take the x axis value and multiply it by the delta x. thanks again!!!
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