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Rimann sum limit of e^x

  • #1

Homework Statement


evaluate integral (0, 1) f(x)=e^x


Homework 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)

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.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
The formula for the sum of a geometric series would be useful.
 

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