1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Riemann sums

  1. Nov 15, 2009 #1
    These questions are ones that my teacher never explained:

    1) if c is a positive integer, then the limit of (1/c)(1/c + 2/c ... + 5c/c) as c approaches infinity can be expressed as

    a) integral of x^2 dx from 0 to 1
    b) integral of 1/x dx from 0 to 5
    c) integral of x dx from -5 to 5
    d) integral of x dx from 0 to infinity
    e) integral of x dx from 0 to 5

    2) the limit as n approaches infinity of (1/n)( (n/1)2 + (n/2)2 + ... + (n/n)2) =

    a) the integral of 1/x2 dx from 0 to 1
    b) the integral of 1/x dx from 0 to 1
    c) the integral of x dx from 0 to 1
    d) the integral of x2 dx from 0 to 1
    e) none of the above

    3) if u is a positive integer, then the limit of (1/u)( (2/u)2 + (4/u)2 + .... + (8u/u)2) can be expressed as

    a) the integral of 8/x2 dx from 0 to 1
    b) the integral of 1/x2 dx from 0 to 1
    c) the integral of 1/x2 dx from 0 to 8
    d) the integral of x2/2 dx from 0 to 8

    I later found out that the answers were e,a, and d in that order but still need an explaination.
     
  2. jcsd
  3. Nov 15, 2009 #2
    Ok. Now I realize where the start and end points for the integral come from. But not the rest.
     
  4. Nov 18, 2009 #3
    Anyone?

    Also, I think its the limit of the sum of .... whatever expression is there.
     
    Last edited: Nov 18, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Riemann sums
  1. Riemann Sums (Replies: 2)

  2. Riemann Sums (Replies: 5)

  3. Riemann sum (Replies: 1)

  4. Riemann sums (Replies: 3)

  5. Riemann Sums (Replies: 10)

Loading...