As it turns out, a good approximation for the error function erf ( x ) is the function tanh ( π 2 x ) .
How good of an approximation? Tell me yourself by finding the total area bounded by these two functions. That is, find the value of:
∫ − ∞ ∞ ∣ ∣ ∣ ∣ erf ( x ) − tanh ( π 2 x ) ∣ ∣ ∣ ∣ d x
Please round to 3 decimal places.
Note: erf ( x ) = π 2 ∫ 0 x e − t 2 d t and tanh ( x ) = cosh ( x ) sinh ( x ) .
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Problem Loading...
Note Loading...
Set Loading...
Solved it via X(PLORE):
f(x)=in(2/sqrt(pi)*exp(-t^2),t=0 to x)
g(x)=tanh(2*x/sqrt(pi))
in(abs(f(x)-g(x)),x=-10 to 10)
So I got 0.100192 ± 5.4e-11.
Rem.: Deviations for larger integration borders are negligible with respect to the necessary decimal places.