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The Maxima on-line user's manual

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Quad_qaws Calculator

Quad_qaws

Function: quad_qaws (<f(x)>, <x>, <a>, <b>, <alpha>, <beta>, <wfun>, [<epsrel>, <epsabs>, <limit>])

Function: quad_qaws (<f>, <x>, <a>, <b>, <alpha>, <beta>, <wfun>, [<epsrel>, <epsabs>, <limit>]) Integration of w(x) f(x) over a finite interval, where w(x) is a certain algebraic or logarithmic function. A globally adaptive subdivision strategy is applied, with modified Clenshaw-Curtis integration on the subintervals which contain the endpoints of the interval of integration.

quad_qaws computes the integral using the Quadpack QAWS routine:

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

The weight function w is selected by <wfun>:

1 w(x) = (x - a)^alpha (b - x)^beta

2 w(x) = (x - a)^alpha (b - x)^beta log(x - a)

3 w(x) = (x - a)^alpha (b - x)^beta log(b - x)

4 w(x) = (x - a)^alpha (b - x)^beta log(x - a) log(b - x)

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_qaws 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;

6 if the input is invalid.

Examples:

          (%i1) quad_qaws (1/(x+1+2^(-4)), x, -1, 1, -0.5, -0.5, 1,
                           epsabs=1d-9);
          (%o1)     [8.750097361672832, 1.24321522715422E-10, 170, 0]
          (%i2) integrate ((1-x*x)^(-1/2)/(x+1+2^(-alpha)), x, -1, 1);
                 alpha
          Is  4 2      - 1  positive, negative, or zero?

pos; alpha alpha 2 %pi 2 sqrt(2 2 + 1)

          (%o2)              -------------------------------
                                         alpha
                                      4 2      + 2
          (%i3) ev (%, alpha=4, numer);
          (%o3)                     8.750097361672829

(%o1)                                true
(%i2) 

Quad_qaws Example

Related Examples

quad_qaws

? quad_qaws;

Calculate

quad_qaws

? quad_qaws;

Calculate