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How to quad("sin(a*sin(x))*sin(x)",0,pi/2)?

From: Francesco Potorti`
Subject: How to quad("sin(a*sin(x))*sin(x)",0,pi/2)?
Date: Wed, 29 Nov 1995 10:25 +0100 (MET)

   > for (i in 1:4)
       quadr ("sin(p1*sin(x)).*sin(x)", 0, pi/2,1.e-6,0,i).Q

   The above is a piece of Rlab code that does what you want (I
   think). The point is: I translated quadr from Matlab source. It is
   written by Kirill K. Pankratov (address@hidden)

I found the following in the matlab archives, form the
contribution/integration directory or some like that, if I am not
wrong.  They should be public domain.  I also have the sources.

Index for integration

nit: <directory>


 Numerical Integration Toolbox
 MATLAB Toolbox for 1-D, 2-D, and n-D Numerical Integration
 The original 1-D routines were obtained from NETLIB and were 
 written by
          Howard Wilson
          Department of Engineering Mechanics
          University of Alabama
          Box 870278
          Tuscaloosa, Alabama 35487-0278
          Phone 205 348-1617
          Email address: HWILSON @ UA1VM.UA.EDU
 The rest of the routines were written by
          Bryce Gardner
          Ray W. Herrick Laboratories
          Purdue University
          West Lafayette, IN 47906
          Phone: 317-494-0231
          Fax:  317-494-0787
          Email:  address@hidden
 These are the general purpose integration routines: 
        quadg.m      -- High accuracy replacement for QUAD and QUAD8 (1-D)
        quad2dg.m    -- 2-D integration over a rectangular region
        quad2dggen.m -- 2-D integration over a general region
        quadndg.m    -- n-D integration over a n-D hyper-rectangular region


misc: <directory>  Integration of math expressions



  DQUAD     Numerically integrates an expression using QUAD.
            I = DQUAD('1/(1+x^3)',a,b) approximates,
                                    |     1    
                                    | ----------- dX
                                    |        3
                                    |  (1 + x  )

      D. Thomas  2/93


  DQUAD     Numerically integrates an expression using QUAD8.
            I = DQUAD8('exp(-x^2)/(1+x^(1/2))',a,b) approximates,
                                  /        2
                                 |  exp(- x )
                                 |  --------- dx
                                 |        1/2
                                /    1 + x
      D. Thomas  2/93


  a = trapz(y,x)

  find the area under the curve y = f(x) using the trapezoidal rule
   x = vector containing the independent variable data points
       the elements of x need not be equally spaced
   y = f(x) = vector of the function values corresponding to the
       elements in x

  a = the area under f(x) in the interval defined by x

 Written by: Duane Hanselman, University of Maine, (207)-581-2246

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