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Simpson's Rule question, which I hate!

  1. Feb 22, 2006 #1

    Hootenanny

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    The question is use simpson's rule with five ordinates to find an approximation for
    [tex] \int_{0}^{4} cos \left[ e^{\frac{1}{2} x} \right] dx [/tex]
    Here are my figures (working in radians)
    [tex] y_0 = 0.540302305 [/tex]
    [tex] y_1 = -0.077846103 [/tex]
    [tex] y_2 = -0.911733914 [/tex]
    [tex] y_3 = -0.228658946 [/tex]
    [tex] y_4 = 0.448356241 [/tex]
    Plugging these into the formula for Simpson's rule gives:
    [tex] \int_{0}^{4} cos \left[ e^{\frac{1}{2} x} \right] dx \approx \frac{1}{3} \left[ (0.540302305 + 0.448356241) + 4(-0.077846103 -0.228658946) + 2(0.448356241 -0.911733914) \right] [/tex]
    This gives - 0.388....... when the answer in the textbook is -0.6869. I know its alot of number crunching but any help would be appreciated.
     
  2. jcsd
  3. Feb 22, 2006 #2
    I don't really know what you are doing there..

    if you just go

    1/3 (y0 + 4y1 + 2y2 + 4y3 + y4) it works properly
     
  4. Feb 22, 2006 #3

    Hootenanny

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    I was using the formula we have been given, you've just expanded the brackets. I've obviously just punched the numbers into my calculator wrong. Thank's.
     
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