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Homework Help: Integral problem.

  1. Jul 18, 2010 #1
    1. The problem statement, all variables and given/known data


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

    f(x)=(lnx)/x

    3 ≤ x ≤ 10

    2. Relevant equations

    See the attachment for the Definition 2.


    3. The attempt at a solution

    ∫ ln(x) / x dx = 1/2 (ln(x))² + C

    10
    ∫ ln(x) / x dx = 1/2 [ (ln(10))² - (ln(3))² ]
    3
     

    Attached Files:

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  2. jcsd
  3. Jul 18, 2010 #2

    Mark44

    Staff: Mentor

    You are supposed to actually use Definition 2, meaning that you are supposed to write the integral as the limit of a summation. The purpose of this exercise is NOT to get a numerical value for the integral.
     
  4. Jul 18, 2010 #3
    Is this the correct answer to the problem?
     

    Attached Files:

  5. Jul 19, 2010 #4
    Actually, I think this is a right answer.
     

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  6. Jul 19, 2010 #5

    vela

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    Almost, but not quite. Show us how you got that. Tell us what you used for Δx and xi first, and show us how you got the summation after you plugged everything in.
     
  7. Jul 19, 2010 #6
    OK, I think I got a mistake. Is that correct now?
     

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  8. Jul 19, 2010 #7

    vela

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    Closer. You forgot the factor of Δx in the summation, and you made an algebra error.
     
  9. Jul 19, 2010 #8
    I see I forgot the factor of Δx. I don't see an algebra error :(
    Olga
     
  10. Jul 19, 2010 #9

    vela

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    In the denominator, you didn't use the correct expression for xi.
     
  11. Jul 19, 2010 #10
    I admire your attention to detail. Thank you a lot.
     
  12. Jul 19, 2010 #11

    Mark44

    Staff: Mentor

    Being good at mathematics requires attention to detail.
     
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