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Reimann's Lawmaajoor Helpp

  1. Mar 20, 2007 #1
    Reimann's Law..maajoor Helpp!!!!!!!

    1. Use Riemann sum ( do NOT use fundamental theorum of Calculus) to calculate
    (integral) b= 1 and a =0 e^x dx


    Attempt:

    (delta x)=b-a/n 1-0/n =1/n
    xi = 1/n

    (integral) b=1 a=0 sigmaf(xi)deltax
    limn->infin sigma f(i/n)1/n
    use eqn to get...limn->infin 1/nsigma{e^(i/n)}
    limn->infin 1/n e^1/ni
    limn->infi 1/ne^1/n n(n+1)/2
    limn->infin 1/n e^1/2(n+1)

    then sub for n (table n | Rn where n =40,100,500,1000,5000 and Rn should be close to 1.72(got that using FTC2)...so the eqn must be wrong :D

    3.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 20, 2007 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Use what equation? This is the crucial part!
    You can rewrite this sum as
    [tex]\frac{1}{n} \sum_{i=0}^n (e^{1/n})^i[/tex]
    That's a geometric series with "common ratio" e1/n: its sum is
    [tex]\frac{1}{n}\frac{1- e^{(n+1)/n}}{1- e^{1/n}}[/tex]

     
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