Numericintegration

[Arno K]

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

  NumericIntegr.hpprgm (Size: 5.85 KB / Downloads: 17)
Edit: Update attachment, now provides exact value, too

[Namir]

Can you please post the listing?

Thanks!

Namir

[Arno K]

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.

[Namir]

Thank you!

:-)

Namir