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    Riemann-Stieltjes

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    Let a(x)=x^3. From the definition, approximate the Riemann-Stieltjes integral....for each of the following partitions

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    https://brainmass.com/math/integrals/riemann-stieltjes-integral-221205

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    Please find the solution in the attachment.

    Solution: Given function f(x) =2x-1 is bounded on [0, 2]. The integrator . We know the partition . So, . The increments and .
    So,
    The approximate value of the R-S integral is 22.

    Let us solve this problem by proving two independent statements.
    First we prove that if then
    and
    To prove this, for a given , there ...

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    This provides an example of approximating the Riemann-Stieltjes integral.

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