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Math Help - sigma notation

  1. #1
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    sigma notation

    divide the specified interval into n=4 subintervals of equal length and then compute using the Area under a curve
    with x^*_kas a left endpoint of each subinterval
    f(x)=3x+1; [2,6]
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  2. #2
    o_O
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    A \approx \sum_{k = 0}^{n} f(x_{k}^*) \Delta x

    Each interval is: \Delta x = \frac{b-a}{n} = \frac{6-2}{4} = 1

    And since we're using left-end points, i.e. x^*_k = x_{k-1}, we have: x_0 = 2, \ x_1 = 3, x_2 = 4, x_3 = 5

    So plugging it all in: A \approx \sum_{k=1}^4 f(x^*_k) \Delta x = \sum_{k=1}^4 f(x_{k-1}) (1) = f(x_0) + f(x_1) + f(x_2) + f(x_3) = \cdots
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