Reimann's Lawmaajoor Helpp

  • Thread starter angel_eyez
  • Start date
  • #1
19
0
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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
961
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)}
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]

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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Related Threads on Reimann's Lawmaajoor Helpp

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
524
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
6
Views
936
Replies
1
Views
1K
  • Last Post
Replies
15
Views
2K
Replies
5
Views
1K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
915
Replies
2
Views
1K
Top