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Math Help - Any one help Upper and Lower sums

  1. #1
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    Any one help Upper and Lower sums

    Can someone show me how to find upper and lower sums and hence solve definite integral of x^3 for [0,2]

    thanks
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  2. #2
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    Quote Originally Posted by jamtheman View Post
    Can someone show me how to find upper and lower sums and hence solve definite integral of x^3 for [0,2]

    thanks
    Do your class notes or textbook contain no reference material? Try reading this: http://www.geometer.org/mathcircles/riemannint.pdf

    Use the example as a model for integrating x^3 over [0, 2]. If you're still stuck, please show what you've tried and where you get stuck.
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  3. #3
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    Well ive found the upper sum easily enough to be (2/n)^4 * [{n(n+1)}/2]^2
    and i wonder could you derive the lower sum simply by knowing the difference and subtracting from the upper sum?
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  4. #4
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    Quote Originally Posted by jamtheman View Post
    Well ive found the upper sum easily enough to be (2/n)^4 * [{n(n+1)}/2]^2
    and i wonder could you derive the lower sum simply by knowing the difference and subtracting from the upper sum?
    No. I would guess that you have derive the lower sum along the same lines that you derived the upper sum. Then take the limit as n --> oo of either one of them.

    By the way, when asking a question you should post what you've been able to do so that people don't spend their time posting things that you already know.
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