1. Not finding help here? Sign up for a free 30min 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!

Need some help with Riemann Sums.

  1. Dec 1, 2008 #1
    Need some urgent help with Riemann Sums.

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

    PART A:

    In all of this question, let I = [tex]\int ^{2}_{-2} f(x)dx [/tex] [tex]where f(x) = -2x + 1 [/tex]

    Evaluate I.

    PART B:

    Use the defintion of the definite integral to evaluate I.
    i.e Riemann Sum.

    2. Relevant equations

    3. The attempt at a solution

    PART A:

    I = [-(2)^2 + (2)] - [-(-2)^2 + (-2)]
    I = -2 + 6 = 4

    Part B is what i am having trouble with.

    Xk = a + k([tex]\Delta x[/tex])
    a = -2


    [tex]\Delta x[/tex] = b-a/n = 2- (-2)/n = 4/n

    so then

    Xk = -2 + 4k/n

    Now the Reimann sum is:

    [tex]\sum f(Xk)(\Delta x)[/tex] = [tex]\sum [-2(-2 + 4k/n) + 1](4/n)[/tex]
    = 4/n [tex]\sum 4 - 8k/n + 1 [/tex]
    = 4/n [tex]\sum -8k/n + 5[/tex]
    = 4/n x -8/n [tex]\sum k[/tex] + [tex]\sum 5[/tex]
    = -32/n2 x [(n)(n+1)/2] + 5n

    Now when i take the limit approaching infinity for that, it doesnt give me 4 as an answer unless im doing something wrong.
    This is where i am stuck at.
  2. jcsd
  3. Dec 1, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Re: Need some urgent help with Riemann Sums.

    Your last two lines start to look pretty goofy. The limit of (4/n)*(5n-8*n(n+1)/2) is 4. Then parentheses start disappearing and numbers are magically factored out. Check it again.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Need some help with Riemann Sums.
  1. Riemann sum help (Replies: 1)

  2. Riemann Sums - Help! (Replies: 0)