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Error function

  1. Mar 30, 2007 #1
    http://en.wikipedia.org/wiki/Error_function

    If you have erf(1.00) and are asked to solve for the approximate value by using the trapezoid rule with n=6, how would you go about doing so?

    Since the function is erf(x) the 'x' goes into the limits of integration but a 't' is used as a variable in the actula function. How do you know what to use for 'u'. Do you simply treat the function as an integral from 0 to 1 and evauluate 'u' from 0 to 1 as well????

    thanks for any help?
     
  2. jcsd
  3. Mar 30, 2007 #2

    Gib Z

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    Homework Helper

    Basically the question is asking to approximate the definite integral:

    [tex]\frac{2}{\sqrt{\pi}}\int_0^1 e^{-x^2} dx[/tex]

    They want you to do it with the trapezoidal rule. Basically construct 6 trapeziums, each with a width of 1/6. The height of the left side of the trapezium should be the same as [itex]e^{-x^2}[/itex] at that point, and the height of the right side should do the same for its point.

    Eg The First trapezium Will have a base from 0 to 1/6. At 0, [itex]e^{-x^2}=1[/itex]. So the height at that point should be 1. At the other side of the trapezium, 1/6, sub in 1/6 into [itex]e^{-x^2}[/itex], and thats the height at that point. You have the two heights of the trapezium, and a base length, now you can find the area.

    Repeat for the other 5 trapeziums.
     
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