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Math Help - Question about Evaluating Integrals using Limits and Sigmas

  1. #1
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    Question about Evaluating Integrals using Limits and Sigmas

    OK, I hope this makes sense.


    So I am taking my second class in calculus but there has been a three year lapse in the time I have taken the first class so I am a little rusty.


    I am trying to create an expression for the area under the curve using limits.

    Specifically, the question asks:


    Use Definition 2 to find an expression for the area under the graph of f as a limit. Do not evaluate the limit.




    Based on that I have garnered the following:


    However, I am lost as to how to proceed. Any help that can explain this step by step would be greatly appreciated.
    Thank you for your time.
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  2. #2
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    Yes, the subintervals are {\Delta}x=\frac{\pi}{2n}

    Right endpoint method:

    x_{k}=\frac{{\pi}k}{2n}

    f(x_{k})=\lim_{n\to {\infty}}\left[\sum_{k=1}^{n}\left(\frac{{\pi}k}{2n}cos(\frac{{\p  i}k}{2n})\right)\frac{\pi}{2n}\right]
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  3. #3
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    Thanks so much for the speedy response!

    I do have a question. I noted that you used k to denote the part that changes in the sigma notation. So, you multiplied delta x by that variable?

    And after that you substitued the resultant product into the original equation?

    Thanks again.
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  4. #4
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    Yes. That is the right end point method
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  5. #5
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    Great, thanks ...

    Quote Originally Posted by galactus View Post
    Yes. That is the right end point method
    Thanks again. This part is starting to make some sense now.
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