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Math Help - proving function is riemann integrable

  1. #1
    xyz
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    proving function is riemann integrable



    the value of a and b is not given. I don't understand how to prove.
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    Quote Originally Posted by xyz View Post


    the value of a and b is not given. I don't understand how to prove.

    Here is a hint. How would you do it for one point?

    i.e let c \in (a,b)

    f(x)=\begin{cases} 0, x \ne c \\ M, x=c \end{cases}

    \int_{a}^{b}f(x)dx

    Let P be the partition \{a,c-\frac{\epsilon}{2|M|},c+\frac{\epsilon}{2|M|},b\}

    Now how would you do it for 2,3 or any finite number?

    I hope this helps.
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    Quote Originally Posted by xyz View Post
    the value of a and b is not given. I don't understand how to prove.
    Do you know that B Riemann was a real person?
    So use capital letters. It is the Riemann integral.

    As to your question.
    Can you find a partition of [a,b] that has each x_j as an endpoint?
    If so, what are the upper and lower sums?
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  4. #4
    xyz
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    I understand the strategy. The textbook gives 2 hints. It says to use theorem 3.1.2 and to use the solution of the previous problem. Unfortunately, I have not been able to find the solution of previous problem. I posted the previous problem at

    http://www.mathhelpforum.com/math-he...ntegrable.html

    but no one gave any idea. If I get an idea out of the previous problem, I can solve this problem because it appears to be related.

    Partition of [a, b] will be (b-a) / n where n is the number of increments. So the partition will look like

    {a, a + (b-a)/n , a + (b-a)/n + (b-a)/n, ......b}
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