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Numericintegration - Arno K - 12-27-2017 11:43 PM
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
RE: Numericintegration - Namir - 12-28-2017 03:46 PM
Can you please post the listing?
Thanks!
Namir
RE: Numericintegration - Arno K - 12-28-2017 04:20 PM
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;Edit: Got that thing with the exact integral implemented, I thought it to be nice to see it for comparing.
RE: Numericintegration - Namir - 12-28-2017 06:22 PM
Thank you!
:-)
Namir