Matlab 5 Numerical Integration Methods

quad

 QUAD   Numerically evaluate integral, low order method.
    Q = QUAD('F',A,B) approximates the integral of F(X) from A to B to
    within a relative error of 1e-3 using an adaptive recursive
    Simpson's rule.  'F' is a string containing the name of the
    function.  Function F must return a vector of output values if given
    a vector of input values.  Q = Inf is returned if an excessive
    recursion level is reached, indicating a possibly singular integral.
 
    Q = QUAD('F',A,B,TOL) integrates to a relative error of TOL.  Use
    a two element tolerance, TOL = [rel_tol abs_tol], to specify a
    combination of relative and absolute error.
 
    Q = QUAD('F',A,B,TOL,TRACE) integrates to a relative error of TOL and
    for non-zero TRACE traces the function evaluations with a point plot
    of the integrand. 
 
    Q = QUAD('F',A,B,TOL,TRACE,P1,P2,...) allows parameters P1, P2, ...
    to be passed directly to function F:   G = F(X,P1,P2,...).
    To use default values for TOL or TRACE, you may pass in the empty
    matrix ([]).

quad8

 
 QUAD8  Numerically evaluate integral, higher order method.
    Q = QUAD8('F',A,B) approximates the integral of F(X) from A to B to
    within a relative error of 1e-3 using an adaptive recursive Newton
    Cotes 8 panel rule.  'F' is a string containing the name of the
    function.  The function must return a vector of output values if
    given a vector of input values.  Q = Inf is returned if an excessive
    recursion level is reached, indicating a possibly singular integral.
 
    Q = QUAD8('F',A,B,TOL) integrates to a relative error of TOL.  Use
    a two element tolerance, TOL = [rel_tol abs_tol], to specify a
    combination of relative and absolute error.
 
    Q = QUAD8('F',A,B,TOL,TRACE) integrates to a relative error of TOL and
    for non-zero TRACE traces the function evaluations with a point plot
    of the integrand.
 
    Q = QUAD8('F',A,B,TOL,TRACE,P1,P2,...) allows coefficients P1, P2, ...
    to be passed directly to function F:   G = F(X,P1,P2,...).
    To use default values for TOL or TRACE, you may pass in the empty
    matrix ([]).

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