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The Maxima on-line user's manual

Algebra Calculator

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Quad_qags Calculator

Quad_qags

Function: quad_qags (<f(x)>, <x>, <a>, <b>, [<epsrel>, <epsabs>, <limit>])

quad_qags(1/x^2,x,1,inf);

Function: quad_qags (<f>, <x>, <a>, <b>, [<epsrel>, <epsabs>, <limit>]) 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 keyword arguments are optional and may be specified in any order. They all take the form key=val. The keyword arguments are:

<epsrel> Desired relative error of approximation. Default is 1d-8.

<epsabs> Desired absolute error of approximation. Default is 0.

<limit> Size of internal work array. <limit> is the maximum number of subintervals to use. Default is 200.

quad_qags returns a list of four elements:

* an approximation to the integral,

* the estimated absolute error of the approximation,

* the number integrand evaluations,

* an error code.

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, epsrel=1d-10);
          (%o1)   [.4444444444444448, 1.11022302462516E-15, 315, 0]

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

(%o1)                                true
(%i2) 

Quad_qags Example

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