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quad_qags

Maxima Function

Calling Sequence

quad_qags (f(x), x, a, b, epsrel, limit)
quad_qags(f,x,a,b,epsrel,limit)

Description

Integration of a general function over a finite interval. quad_qags implements globally adaptive interval subdivision with extrapolation (de Doncker, 1978) by the Epsilon algorithm (Wynn, 1956).

quad_qags computes the integral

integrate (f(x), x, a, b)

The function to be integrated is f(x), with dependent variable x, and the function is to be integrated between the limits a and b.

The integrand may be specified as the name of a Maxima or Lisp function or operator, a Maxima lambda expression, or a general Maxima expression.

The optional arguments epsrel and limit are the desired relative error and the maximum number of subintervals, respectively. epsrel defaults to 1e-8 and limit is 200.

quad_qags returns a list of four elements:

The error code (fourth element of the return value) can have the values:

0

no problems were encountered;

1

too many sub-intervals were done;

2

excessive roundoff error is detected;

3

extremely bad integrand behavior occurs;

4

failed to converge

5

integral is probably divergent or slowly convergent

6

if the input is invalid.

Examples:

(%i1) quad_qags (x^(1/2)*log(1/x), x, 0 ,1);
(%o1)   [.4444444444444448, 1.11022302462516E-15, 315, 0]

Note that quad_qags is more accurate and efficient than quad_qag for this integrand.

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