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Rimann sum limit of e^x

  1. Nov 24, 2009 #1
    1. The problem statement, all variables and given/known data
    evaluate integral (0, 1) f(x)=e^x


    2. Relevant equations
    integral (a,b) f(x) dx = lim n-> infinity, sum of (i = 1, n) f(xi*)Deltax
    where :
    delta x = b-a/n
    xi*= a+(delta xi)

    3. The attempt at a solution

    Deltax= 1-0/n = 1/n

    xi*=0+(1/n)i = i/n

    f(xi*)Deltax = (e^(i/n)) (1/n)

    SUM OF:(e^(i/n)) (1/n)

    (1/n) SUM OF:((e^(i/n))

    i hope i was somewhat correct up till this point. Now i have no idea what summation formula to use here as the basic k=kn , i=n(n+1)/n and i^2=n(n+1)(2n+1)/6
    dont seem to be very useful.
     
  2. jcsd
  3. Nov 24, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The formula for the sum of a geometric series would be useful.
     
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