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Limits of Integration

  1. Nov 22, 2013 #1

    Qube

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    1. The problem statement, all variables and given/known data

    http://i.minus.com/jJQzZXoxXFqEB.png [Broken]

    2. Relevant equations

    (b-a)/n = Δx

    3. The attempt at a solution

    I know how to express the sum as an integral .. almost. It is the integral of cos(2+x) with respect to x. However, what are my bounds of integration? I know that b-a must equal 1, but I don't think I can pick any arbitrary b and a that are just one counting number apart, right?
     
    Last edited by a moderator: May 6, 2017
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  3. Nov 22, 2013 #2

    LCKurtz

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    Write down the ##x_i## in this problem for ##i=1..n##. That will give you an idea of what interval is being used.
     
    Last edited by a moderator: May 6, 2017
  4. Nov 22, 2013 #3

    Dick

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    Of course, you can't. You are identifying i/n with x. What are the limits of i/n as i goes from 1 to n? Now what happens if you take the limit?
     
    Last edited by a moderator: May 6, 2017
  5. Nov 22, 2013 #4

    Qube

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    I'm going from 1/n to 1.

    It seems as if when I take the limit as n approaches infinity 1/n becomes 0. The limit of a constant is the constant, so it appears my interval is 0 to 1.
     
  6. Nov 22, 2013 #5

    LCKurtz

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    So the limit of that sum as ##n\to \infty## is ...?
     
  7. Nov 22, 2013 #6

    Qube

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    The integral of cos(2 + x) with respect to x and with bounds as 0 and 1.
     
  8. Nov 22, 2013 #7

    LCKurtz

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