Line integral and curvilinear integral
05-15-2015, 08:17 PM (This post was last modified: 01-17-2021 05:14 PM by salvomic.)
Post: #1
 salvomic Senior Member Posts: 1,392 Joined: Jan 2015
Line integral and curvilinear integral
hi all,
here there are two programs (CAS) to calculate Line integral (for vectorial functions fields) and Curvilinear Integral (for scalar functions).

intcur: INPUT a scalar function (x,y,z), a parametric form of a curve [r(t), r(t), r(t)], lower and high bound and the programs returns curvilinear integral
intlin: INPUT a vectorial function, a parametric form of a curve (as above), lower and high bound and the program returns linear integral.

These programs work with 2 or 3 components (parametric expression: [r1(t), r2(t), r3(t)] or [r1(t), r2(t)])...

Examples:
1.0 to find the curvilinear integral of z in a circle (parametric: x=COS(t), y=SIN(t), z=t) from 0 to 2π
intcur(z, [COS(t), SIN(t), t], 0, 2*π) -> 2*√2*π^2
2. to find the line integral of F=‹x*SIN(y), y› along the path ‹t, t^2› from -1 to 2
intlin([x*SIN(y), y], [t, t^2], -1,2) -> (15/2)+(COS(1)-COS(4))/2

Enjoy!

Salvo Micciché

Code:
 #cas intcur(args):=     BEGIN     local argv,argc, a, b;     local f, r, dr, ft, s,t;     purge(t);     argv:=[args];     argc:=size(argv);     IF argc !=4 THEN     return "Input:f(x,y,z), [r(t),r(t),r(t)] ,low, high";      ELSE     f:=argv(1);     r:=argv(2);     a:=argv(3);     b:=argv(4);     dr:=diff(r,t);     s:= size(argv(2));     ft:= IFTE( s==3, subst(f,[x,y,z]=r), subst(f,[x,y]=r) );     return int(dot(ft,l2norm(dr)),t,a,b);     END; END; #end

...
Code:
 #cas intlin(args):= BEGIN local argv, argc, a, b; local f, r, dr, ft,s, t; purge(t); argv:=[args]; argc:=size(argv); IF argc !=4 THEN return "Input:[x,y,z], [r(t),r(t),r(t)] ,low, high";   ELSE f:=argv(1); r:=argv(2); a:=argv(3); b:=argv(4); dr:=diff(r,t); s:= size(argv(2)); ft:= IFTE( s==3, subst(f,[x,y,z]=r), subst(f,[x,y]=r) ); return int(dot(ft,dr),t,a,b); END; END; #end

EDIT: put above a slightly new code, in which t is a local variable that's now purged first to being used in the integral calculus, to avoid to leave a global variable in CAS Vars.

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
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