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Math Help - Definite integral that is equal to Riemann sums

  1. #1
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    Definite integral that is equal to Riemann sums

    The problem is limit as n goes to infinity, riemann sum from i=1 to n of (2/n)(1+(2i/n))^1/2

    The problem I have i getting rid of the ^1/2? I was thinking that I could evaluate the sums under the square root like Riemann sum of 1 + Riemann sum of 2i/n.all under the square root. I don't think that's how I'm suppose to do it.
    Any help is greatly appreciated.

    The 4 integrals to choose from are

    integral from 1 to 2 f(x) = (1+x)^1/2dx
    integral from 1 to n f(x) = (x)^1/2dx
    integral from n to 2 f(x) = (1+x)^1/2dx
    integral from 1 to 3 f(x) = (x)^1/2dx

    What does the does the integral from 1 to the n mean?
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  2. #2
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    Re: Definite integral that is equal to Riemann sums

    Quote Originally Posted by KenAdams View Post
    The problem is limit as n goes to infinity, riemann sum from i=1 to n of (2/n)(1+(2i/n))^1/2

    The problem I have i getting rid of the ^1/2? I was thinking that I could evaluate the sums under the square root like Riemann sum of 1 + Riemann sum of 2i/n.all under the square root.
    Any help is greatly appreciated.
    The 4 integrals to choose from are
    integral from 1 to 2 f(x) = (1+x)^1/2dx
    integral from 1 to n f(x) = (x)^1/2dx
    integral from n to 2 f(x) = (1+x)^1/2dx
    integral from 1 to 3 f(x) = (x)^1/2dx
    What does the does the integral from 1 to the n mean?
    I do not see in the list.
    But \int_1^3 {\sqrt {1 + x} dx} will work.

    I think there is a typo in the last one.
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    Re: Definite integral that is equal to Riemann sums

    Thank you, but how did you figure it out.? I'm stuck with removing that square root.
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    Re: Definite integral that is equal to Riemann sums

    Quote Originally Posted by KenAdams View Post
    Thank you, but how did you figure it out.? I'm stuck with removing that square root.
    Look at this. But sure to click show steps.
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    Re: Definite integral that is equal to Riemann sums

    I know how to find the integrals but I don't know how to solve the Riemunns sums?
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    Re: Definite integral that is equal to Riemann sums

    Quote Originally Posted by KenAdams View Post
    I'm stuck with removing that square root.
    Quote Originally Posted by KenAdams View Post
    I know how to find the integrals but I don't know how to solve the Riemunns sums?
    In your first reply you said that it was the square root giving you trouble.
    Now you seem confused about Riemann Sums. In the future, please make your questions clear.

    The interval is [1,3] its length is 3-1=2. Divide \frac{2}{n}.

    So the \Delta_x=\frac{2}{n}, and the partition points x_k=(1+k\Delta_x) where k=1,2,\cdots,n

    Thus \sum\limits_{k = 1}^n {\sqrt {(1 + {x_k})} {\Delta _x}}
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