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Math Help - Simpson's Approximation

  1. #1
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    Simpson's Approximation

    I am not getting the correct answer for this so I'm sure I'm messing up some arithmetic or missing a step. Any help would be appreciated.

    Use Simpson's Approx. for: \int^1_0 \frac{tan(x)}{x}dx\;n=10
    \frac{b-a}{n}= \frac {1-0}{10}=.1=\Delta x
    \frac{\Delta x}{3}=\frac{1}{30}

    Plugging in 0,.1,.2,...,.9,1 into the function I get
    S_{10}=\frac{1}{30}(0+4(1.003)+2(1.0136)+4(1.0311)  +2(1.0570)+4(1.0930)+2(1.1402)+4(1.2033)+2(1.2870)  +4(1.4002)+1.5574)

    This equals roughly 1.11585

    However, when I evaluate the integral

    \int^1_0 \frac{tan(x)}{x}dx

    I end up with 1.14915. Where is the discrepancy coming from? Thanks for the help!
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  2. #2
    Grand Panjandrum
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    Re: Simpson's Approximation

    Quote Originally Posted by Bowlbase View Post
    I am not getting the correct answer for this so I'm sure I'm messing up some arithmetic or missing a step. Any help would be appreciated.

    Use Simpson's Approx. for: \int^1_0 \frac{tan(x)}{x}dx\;n=10
    \frac{b-a}{n}= \frac {1-0}{10}=.1=\Delta x
    \frac{\Delta x}{3}=\frac{1}{30}

    Plugging in 0,.1,.2,...,.9,1 into the function I get
    S_{10}=\frac{1}{30}(0+4(1.003)+2(1.0136)+4(1.0311)  +2(1.0570)+4(1.0930)+2(1.1402)+4(1.2033)+2(1.2870)  +4(1.4002)+1.5574)

    This equals roughly 1.11585

    However, when I evaluate the integral

    \int^1_0 \frac{tan(x)}{x}dx

    I end up with 1.14915. Where is the discrepancy coming from? Thanks for the help!
    Reconsider the value of the integrand at x=0.

    CB
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  3. #3
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    Re: Simpson's Approximation

    Tan(0)/0 should be 0 no? Or, at the very least, undefined.

    I should add that I'm using a calculator and Wolframalpha alpha to evaluate. Is this just a reasonable amount of error from the approximation?
    Last edited by Bowlbase; November 15th 2011 at 07:13 AM.
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  4. #4
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    Re: Simpson's Approximation

    Okay, I got it.

    I needed to use limit as x approaches 0 = 1. That gets me a lot closer to the answer.
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