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Math Help - Estimating With Finite Sums

  1. #1
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    Estimating With Finite Sums

    can somebody explain to me how to do the following problem?

    y = 2x-x^2 [0,2]

    partition [0,2] into 4 subintervals and show the four rectangles that LRAM uses to approximate the area of the function. Compute the LRAM sum without a calculator.


    thanks for any help
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  2. #2
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    Quote Originally Posted by turtle View Post
    can somebody explain to me how to do the following problem?

    y = 2x-x^2 [0,2]

    partition [0,2] into 4 subintervals and show the four rectangles that LRAM uses to approximate the area of the function. Compute the LRAM sum without a calculator.


    thanks for any help
    I assume you need to find,
    \int_0^2 2x-x^2dx

    The length of the interval is 2.
    And there are 4 rectangles, so the width of each one is,
    \Delta x=\frac{2}{4}=.5

    Now form the sum,
    \sum_{k=1}^n f(a+k\Delta x)\Delta x
    But,
    \Delta x=.5
    a=0
    n=4
    f(x)=2x-x^2
    (Note, k is a running value. It has no specific value. It simply are all the integers between 1 and 4).
    Thus, f(a+k\Delta x)=f(.5k)
    Thus,
    \sum_{k=1}^4 f(.5k)\Delta x
    Thus,
    \sum_{k=1}^4 [2(.5)k-(.5k)^2](.5)
    Thus,
    \sum_{k=1}^4 (k-.25k^2)(.5)
    Add,
    (1-.25(1)^2)(.5)+(2-.25(2)^2)(.5)+(3-.25(3)^2)(.5)+(4-.25(4)^2)(.5)
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