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This program uses an hybrid of CAS and Home-program to compute the integral of an via input entered function, the borders and intervals to compute diverse numeric integrals. It can easily be extended to other formulas, the included ones are those I sometimes need to check hand-calculations made by my pupils.
Arno
[attachment=5492]
Edit: Update attachment, now provides exact value, too

Can you please post the listing?

Thanks!

Namir

Its a little bit long, but here it is:

Code:

#cas

integr(g,a,b):=

BEGIN

logal h,x;

g:=expr(g);

IF type(g)==DOM_SYMBOLIC THEN

     g:=unapply(g,x);

     END;

h:=int(g(x),x,a,b);

RETURN (h);

END;

#end

#cas

simpsonint(g,a,b,n):=

BEGIN

local l,l1;

g:=expr(g);

IF even(n) THEN

IF (type(g)==DOM_SYMBOLIC  OR type(g)== DOM_FUNC)

  THEN 

   l:=MAKELIST(X,X,a,b,(b-a)/n);

     IF type(g)==DOM_SYMBOLIC THEN

     g:=unapply(g,x);

     END;

   l:=apply(g,l);

   l1:=MAKELIST(even(X)+1,X,1,n+1);

 return (2*DOT(l,l1)-g(a)-g(b))*(b-a)/(3*n);

   ELSE return ("f must be symbolic or function!");

  END;

ELSE return "n must be even!";

END;

END;

#end

#cas

trapezregel(g,a,b,n):=

BEGIN

local l;

g:=expr(g);

IF (type(g)==DOM_SYMBOLIC  OR type(g)== DOM_FUNC)

  THEN 

   l:=MAKELIST(X,X,a,b,(b-a)/n);

     IF type(g)==DOM_SYMBOLIC THEN

     g:=unapply(g,x);

     END;

   l:=apply(g,l);

   return (2*ΣLIST(l)-g(a)-g(b))*(b-a)/(2*n);

   ELSE return ("f must be symbolic or function!");

  END;

END;

#end

#cas

rightsum(g,a,b,n):=

BEGIN

local l;

g:=expr(g);

IF (type(g)==DOM_SYMBOLIC  OR type(g)== DOM_FUNC)

  THEN 

   l:=MAKELIST(X,X,a,b,(b-a)/n);

     IF type(g)==DOM_SYMBOLIC THEN

     g:=unapply(g,x);

     END;

   l:=apply(g,l);

   return (ΣLIST(l)-g(a))*(b-a)/n;

   ELSE return ("f must be symbolic or function!");

  END;

END;

#end

#cas

leftsum(g,a,b,n):=

BEGIN

local l;

g:=expr(g);

IF (type(g)==DOM_SYMBOLIC  OR type(g)== DOM_FUNC)

  THEN 

   l:=MAKELIST(X,X,a,b,(b-a)/n);

     IF type(g)==DOM_SYMBOLIC THEN

     g:=unapply(g,x);

     END;

   l:=apply(g,l);

   return (ΣLIST(l)-g(b))*(b-a)/n;

   ELSE return ("f must be symbolic or function!");

  END;

END;

#end

EXPORT NumericIntegr()

BEGIN

local a,N,f,b;

N:=12; a:=1;b:=3;

f:='X^2';

   if input(

     {{f,[8],{20,70,0}},

     {a,[0],{20,30,1}},

     {b,[0],{20,30,2}},

     {N,[0],{20,30,3}}},

     "Enter Data",

     {"f(X)=", "a= ", "b= ","N= "

      },

     {

       "Enter the function, upper case X!",

       "Enter the starting point",

       "Enter the endpoint",

       "Enter the amount of intervals"

     },

     {f,a,b,N}

   )

then

f:=lower(string(f));

PRINT();

PRINT("Simpsonsum:   "+simpsonint(f,a,b,N));

PRINT("Trapezoidsum:    "+trapezregel(f,a,b,N));

PRINT("Rectangleleft:  "+leftsum(f,a,b,N));

PRINT("Rectangleright: "+rightsum(f,a,b,N));

PRINT("Integral:"+integr(f,a,b));

return;

end;

END;

Arno
Edit: Got that thing with the exact integral implemented, I thought it to be nice to see it for comparing.

Thank you!

:-)

Namir

Arno K

Namir

Arno K

Namir