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Riemann Sum from Indefinite Integral

  1. Sep 4, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider the integral,

    [itex]\int _3 ^7 (\frac{3}{x} + 2) dx[/itex]

    a) Find the Riemann Sum for this integral using right endpoints and n=4.

    b) Find the Riemann Sum for this integral using left endpoints and n=4.

    2. Relevant equations
    The sum,
    [itex]\sum^{n = 4} (\frac{3}{x} + 2)[/itex]

    The graph,
    b0de2dab.jpg

    f(x) (white)
    x = 3 (blue)
    x = 7 (blue)
    y = 3 (yellow)
    y = f(7) (red)


    3. The attempt at a solution

    The right endpoint would be (7, f(7))
    The product of the sum would be the area of the box, so
    [itex]f(7) * 4[/itex]
    (this answer is in an acceptable format for my teacher)

    The left endpoint would be (3,F(3))
    The product of the sum would be the area of the box, so
    [itex]f(3) * 4 = 12[/itex]

    But I'm wrong, evidently.

    Thanks in advance, guys!
     
    Last edited: Sep 4, 2011
  2. jcsd
  3. Sep 4, 2011 #2

    dynamicsolo

    User Avatar
    Homework Helper

    The condition n = 4 in the two parts of the problem means that you are to divide the interval from x = 3 to x = 7 into four equal parts, and then find the total area of the four rectangles you are to construct for the Riemann sum, using either the "Right Endpoint" or "Left Endpoint Rule".
     
  4. Sep 4, 2011 #3
    You're right! I can't believe I forgot this. Thanks dynamicsolo!

    btw, That's some great advice in your signature.

    For future reference,

    [itex]\sum_i^4 \frac{3}{x} + 2 \rightarrow[/itex]

    Right
    [itex]
    (i)(\frac{n}{7-3})[f(3) + f(4) + f(5) + f(6)]
    [/itex]

    Left
    [itex]
    (i)(\frac{n}{7-3})[f(7) + f(4) + f(5) + f(6)]
    [/itex]
     
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