Different result in Integral

[compsystems]

sorry for my bad English

Quote:In my opinion some functions really are not necessary in a cas.

if are necessary, other educational software with CAS, they incorporate them.

Some ideas that I proposed in this forum, for example are incorporated in geogebra (aka GG), they are taking the xcas (symbolic computation engine) and adapting it to a more standard and educational environment, which is also purpose on the hp-prime

Example, the default xcas not include variable solution in the responses, this was included in GG

in geogebra, CAS view // $# == entry(#)

1: {x^2-10*x+y^2+8=0,x*y^2+x-10*y+8=0 }

2: Solve( $1,{x, y}) [enter] returns
{{x = 1, y = 1}, {x = 2.193439415415, y = 3.020466468123}} // an output more explicit

3: Substitute( $1,{x = 1, y = 1}) [enter] returns
{0 = 0, 0 = 0} // solutions are exact

4: Substitute( $1,{x = 2.193439415415, y = 3.020466468123}) [enter] returns
{1.52671476535e−12 ~= 0, −3.22853213847e−12) ~= 0} // solutions are approximate

in HP-Prime CAS view

{x^2-10*x+y^2+8=0,x*y^2+x-10*y+8=0 }

solve( Ans,{x, y}) [enter] returns
{[2.19343941542,3.02046646812],[1.,1.]} //naked eye a student does not understand the output, is a matrix?, list, list/vector ....

subst( {x^2-10*x+y^2+8=0,x*y^2+x-10*y+8=0 } ,{x = 1, y = 1}) [enter] returns
{0 = 0, 0 = 0}

2: I suggest in the hp-prime a command to compare two parts

in GG is the operator =?
{0 =? 0, 0 =? 0} returns ->
{true, true }

functions that are very useful, that the hp-prime development team not want to be incorporated, your answer is this can be done by user command, but the idea is that they are built into the system,geogebra think of the student, not the programmer

the operator =? in GG is Hp-prime
subst(expression, '=', '==' )

subst({0 = 0, 0 =0}, '=', '==' ) returns {1,1} 1 is not so explicit to true
a patch
if (subst(expression, '=', '==' )==1 then return "true"; else "false"; end;...

CAS must be expert systems, not the student is an expert in programming, an expert system resembles a human being, if I ask even human, three equals three, the will not answer 1, the vast majority answered true, 1 is for robots, and students are not robots.

I share more the philosophy of geogebra , take the excellent work of Bernard Parisse (xCAS) but makes it more human and knowledgeable and dedicated students and math teachers =)