# Help System (web edition)

```Integral of function f(x) in the interval (a,b) is computed using
Simpson's rule by the `integral' statement of the form
<variable>=integral(f(x))from(a)to(b)
or in extended forms
<variable>=integral(f(x))from(a)to(b)eps(eps) ,
<variable>=integral(f(x))from(a)to(b)eps(eps)n(n) .
The original range (a,b) is split by 2^n equidistant points using
n=1,2,3,... until the relative error is <eps or the optional n value
is achieved. Default values are eps=1e-10, n=12.
Examples:
................................................................................
a=0 b=1 eps=0.0001 pi=3.141592653589793 infinity=10
I1=integral(x^2)from(a)to(b)eps(eps)
I2=integral(exp(-x*x/2)/sqrt(2*pi))from(-infinity)to(0)
I1.=0.33333333333333
I2.=0.5

................................................................................
Number of prime integers less than N ( here N=1000000 ) can be roughly
approximated by the integral

integral(1/log(x))from(2)to(N)eps(0)n(17)=78627.636537002

while the true number is 78498.