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Homework Help: Simpson & trapezium rule

  1. Mar 2, 2005 #1
    Why should I use the simpson or trapezium rule when calculating the area under a curve? It is much easier and accurate when using integration the ordinary way :confused:
  2. jcsd
  3. Mar 2, 2005 #2
    In general, you must approximate something that is either difficult or impossible to do analytically. Not many functions can be "integrated the ordinary way." Most functions can be approximated, though.

  4. Mar 2, 2005 #3
    Can you give me an example of a function that is impossible to integrate analytiacally?
  5. Mar 2, 2005 #4
    [tex]\mbox{Si}(z) \equiv \int_0^z \frac{\sin{t}}{t} dt[/tex]

    Last edited: Mar 2, 2005
  6. Mar 2, 2005 #5


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    [tex]\int_0^1 e^{x^2}dx[/tex]

    "Almost all" integrals cannot be done analytically.
  7. Mar 2, 2005 #6


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    However, "almost all" integrals you learn about in your first year can be solved by the "ordinary" way..:wink:
  8. Mar 2, 2005 #7
    Perhaps more tangable to you in the near future: If you are learning Simson's rule now, you will most likely get to arclength very shortly. You will also find then that sometimes evaluating an integral like


    Can be very difficult if [itex]\frac{dy}{dx}[/itex] is long or confusing.
    Last edited: Mar 2, 2005
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