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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.

    --J
     
  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]

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

    HallsofIvy

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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

    arildno

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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

    [tex]\int_a^b\sqrt{1+{\left(\frac{dy}{dx}\right)}^2}{dx}[/tex]

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