kill(all)$

maxima : integration in combination with vector operations inside(div,grad). version 1.0
peter.vlasschaert@gmail.com , 23/09/2021

load packages , option
==================

load(vect)$/* don't forget this :div,grad,curl*/
load(lrats)$

argument : zz
===========

→ function for the vector .

ax: 2*x*y;
ay:2*x*y^2;
az:2*z^3*x*y;

→  vector = zz

zz:[ax,ay,az];

assume(y>0,z>0);/* integration range for integration in general */

integration : vector operatorion inside integral.

→ div  operator inside integration

sa:'integrate('integrate('integrate(vectorsimp(express(div(zz))),x,0,y),y,0,z),z,0,7);

1e) method :step evaluation (sa)
=========================

→ differentation evaluation :first 

sb:ev(sa,diff);

→ integration evaluation :second

sc:ev(sb,integrate);

2e) method :step evaluation (sa)
=========================

sd:ev(sa,nouns);

sd1:float(sd);

check : sc ? sd
============

is(sc=sd);

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remvalue(x,y,z) $  /* don't forget this : otherwise wrong ,result:error */

rem : kill(x,yz) gives problems

zzz:x^2*y^5*z;/*scalar field */

→grad & div  operator inside integration ( scalar :vector field)

→ grad 

→  method :1

grad(zzz)=express(grad(zzz)),expandall;

→ method : 2 , 'used inside integration sign'

grad(zzz)=vectorsimp(express(grad(zzz)));

sa1:'integrate('integrate('integrate(vectorsimp(express(grad(zzz))),x,0,y),y,0,z),z,0,7);

sb1:ev(sa1,nouns);/*result :vector*/

sb1a:float(sb1);/*result :vector*/

→grad & div  : combination laplacian :∇.∇(zzz) =∇^2(zzz)

→ method 1

div(grad(zzz))=express(div(grad(zzz))),expandall;

→ method : 2 , 'used inside integration sign'

sb2a:div(grad(zzz))=vectorsimp(express(div(grad(zzz))));

sb3a:rhs(sb2a);

sa2:'integrate('integrate('integrate(vectorsimp(express(div(grad(zzz)))),x,0,y),y,0,z),z,0,7);

sb2:ev(sa2,nouns);/*result :value*/

sb22:float(sb2);/*result :value*/

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sa4:'integrate('integrate('integrate(sb3a,x,0,y),y,0,z),z,0,7);
sa5:ev(sa4,nouns);

check: sb2 & sa5
------------------------

is(sb2=sa5);

-----------------------------------------------------------------------------------------------------------------------------------------------------------

sa6:'integrate('integrate('integrate(rhs(sb2a),x,0,y),y,0,z),z,0,7);

sa7:ev(sa6,nouns);

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