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Math Help - riemann sum

  1. #1
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    riemann sum

    I need to find what definite integral is approximated by \sum_{i=1}^{50} (\frac{i}{50})^2\frac{1}{50} on the interval [0,1]

    the answer seems to be \int_0^1 x^2dx but why is it not \int_0^1\frac{x^2}{50^3}dx

    Do I only concern myself with what is happening to i or whatever variable is used, i, k etc etc

    thanks
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  2. #2
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    Re: riemann sum

    the 1/50 is the dx
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  3. #3
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    Re: riemann sum

    I kind of get it, but why not \int_0^1 \frac{x^2}{50^2} dx
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  4. #4
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    Re: riemann sum

    Quote Originally Posted by Jonroberts74 View Post
    I kind of get it, but why not \int_0^1 \frac{x^2}{50^2} dx
    x[i] = i dx

    x[i]2 = (i dx)2

    you have a further dx from the integral itself and as dx = 1/50 you end up with

    \sum _{i=1}^{50} \left(\frac{i}{50}\right)^2 \frac{1}{50}
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