kill(all)$

maxima:programming integration unit_step,load(abs_integrate),version 1.0
peter.vlasschaert@gmail.com,06/02/2022

use : defint,integrate → integration .

integration  :
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assume(a>0,s>0);

rem : s ,laplace Transform

p1:'integrate(2*x^3,x,-a,a) =integrate(2*x,x,-a,a) ;

ust(tt):=if tt<0 then 0 else 1;

usv:ust(t);

p2:'integrate(f(t)*exp(-s*t),t,-a,a) =integrate(f(t)*exp(-s*t),t,-a,a);

p2a:subst([f(t)=t],p2);

p2b:lhs(p2a) = ev(rhs(p2a),nouns);

How to use:load (abs_integrate) .
========================

→ declaration : use unit_step.

c:unit_step(t);

assume(k>0);

→ without abs_integrate

defint(t*exp(-s*t)*c,t,-k,inf);

limit(%,k,inf,minus);

integrate(t*exp(-s*t)*c,t,-k,inf);

limit(%,k,inf,minus);

→ with  abs_integrate

load (abs_integrate) $

p1:defint(t*exp(-s*t)*c,t,-k,inf);

p2:integrate(t*exp(-s*t)*c,t,-k,inf);

rem : {p1 & p2}, laplace transform  : t <-> 1/s^2, find also tables in books,

problem : if construction inside.(not allowed)

integrate(t*exp(-s*t)*usv,t,-k,inf);

other example : abs_integrate. "load"

e : unit_step(t) - 2*unit_step(t - 1) $
integrate (e, t, a, b);

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