Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Error function

  1. Mar 30, 2007 #1

    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

    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook