intg - definite integral

Calling Sequence

[v,err]=intg(a,b,f [,ea [,er])

Parameters

• a,b : real numbers
• f : external (function or list or string)
• ea, er : real numbers
• ea : absolute error required on the result. Default value: 0
• er : relative error required on the result. Default value: 1.d-8
• err : estimated absolute error on the result.

Description

intg(a,b,f) evaluates the definite integral from a to b of f(t)dt. The evaluation hopefully satisfies following claim for accuracy: abs(I-v)<= max(ea,er*abs(I)) where I stands for the exact value of the integral.

f is an external :

If f is function its definition must be as follows y = f(t)

If f is a list the list must be as follows: list(f,x1,x2,...) where f is a function with calling sequence f(t,x1,x2,...).

If f is a string it refers to a the name of a Fortran subroutine (see source code of fintg.f)

Examples

deff('[y]=f(x)','y=x*sin(30*x)/sqrt(1-((x/(2*%pi))^2))')
exact=-2.5432596188;
abs(exact-intg(0,2*%pi,f))
// See file routines/default/Ex-intg.f 
abs(exact-intg(0,2*%pi,'intgex'))
 

See Also

intc  intl  inttrap  intsplin  ode