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Math Help - Reimann Sum Setup

  1. #1
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    Reimann Sum Setup

    Im having trouble setting up this Reimann Sum. The question is
    Find the Riemann sum for f(x) = sin(x) over the interval [0, 2π],

    where x0 = 0, x1 = π/4, x2 = π/3, x3 = π, and x4 = 2π, and

    where c1 = π/6, c2 = π/3, c3 = 2π/3, and c4 = 3π/2. (Round your answer to three decimal places.)

    So heres what i understand. n = 4, so there are 4 rectangles of uneven size. x0 - x4 are the given intervals.

    I m guessing i should take \sum_{i=1}^{n} f(c_i)\Delta{x_i} and set it up like this \sum_{n=0}^{2\pi}sin(c_i)\Delta{x_i}.

    But thats where im stuck. Do i evaluate each right end point times \Delta{x_i} and add them up? Does \Delta{x_i} = \frac{2\pi}{n}i or \frac{2\pi}{4}i



    Any help is greatly appreciated.
    Last edited by petenice; November 30th 2012 at 08:17 AM.
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  2. #2
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    Re: Reimann Sum Setup

    Quote Originally Posted by petenice View Post
    I m guessing i should take \sum_{i=1}^{n} f(c_i)\Delta{x_i} and set it up like this \sum_{n=0}^{2\pi}sin(c_i)\Delta{x_i}.
    You can do better than that.

    \sum\limits_{k = 1}^4 {\sin \left( {c_k } \right)\left( {x_k  - x_{k - 1} } \right)}
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