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Math Help - definite integral....finding the function

  1. #1
    Member mybrohshi5's Avatar
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    definite integral....finding the function

    The following sum
     \frac{1}{1+\frac{3}{n}} \cdot \frac{3}{n} + \frac{1}{1+\frac{6}{n}} \cdot \frac{3}{n} + \frac{1}{1+\frac{9}{n}} \cdot \frac{3}{n} + \ldots + \frac{1}{1+\frac{3 n}{n}} \cdot \frac{3}{n}
    is a right Riemann sum for a certain definite integral  \int_1^b f(x)\, dx
    using a partition of the interval [1,b] into n subintervals of equal length.
    i found b to be 4 but i cannot figure out what f(x) is.
    i thought it was 1/(1+x) but thats not it =(
    help please. thank you
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  2. #2
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    Quote Originally Posted by mybrohshi5 View Post
    The following sum
     \frac{1}{1+\frac{3}{n}} \cdot \frac{3}{n} + \frac{1}{1+\frac{6}{n}} \cdot \frac{3}{n} + \frac{1}{1+\frac{9}{n}} \cdot \frac{3}{n} + \ldots + \frac{1}{1+\frac{3 n}{n}} \cdot \frac{3}{n}
    is a right Riemann sum for a certain definite integral  \int_1^b f(x)\, dx
    using a partition of the interval [1,b] into n subintervals of equal length.
    i found b to be 4 but i cannot figure out what f(x) is.
    i thought it was 1/(1+x) but thats not it =(
    help please. thank you

    I think it is f(x)=\frac{1}{x} in the interval [1,4]: they're taking the right extreme points in every subinterval and evaluate there the function: at 1+\frac{3}{n}\,,\,1+\frac{6}{n}\,,...etc.

    Tonio
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