Different result in Integral
09-06-2016, 01:45 PM (This post was last modified: 09-06-2016 05:21 PM by jrozsas.)
Post: #1
 jrozsas Member Posts: 158 Joined: Nov 2014
Different result in Integral
In integral: ∫√(2x+1)dx
The expected answer is: 1/3 (2x+1)^3/2
But HP Prime show:

How to present the result of the way indicated?(1/3 (2x+1)^3/2)
I Now:

But, I need HP Prime presents the results so. Anyone know how to get the results as expected?

Leo

09-08-2016, 12:42 PM
Post: #2
 jrozsas Member Posts: 158 Joined: Nov 2014
RE: Different result in Integral
Anyone have any suggestions? Is any setup calculator?

Leo

09-08-2016, 08:42 PM
Post: #3
 Arno K Senior Member Posts: 450 Joined: Mar 2015
RE: Different result in Integral
Sorry, but I tried some standard algebraic tricks on your problem and went through my list of commands for the prime to see if there is the possibility to "collect", there seems to no other possibility than looking at the result and doing it by hand.
Arno
09-08-2016, 09:13 PM (This post was last modified: 09-08-2016 09:20 PM by compsystems.)
Post: #4
 compsystems Senior Member Posts: 1,329 Joined: Dec 2013
RE: Different result in Integral
(1/3)*(2*x+1)^(1/2)*(2*x+1) -> (2*x*√(2*x+1)+√(2*x+1))/3

But

[Shift]+[()]+ (1/3)*(2*x+1)^(1/2)*(2*x+1) -> (2*x+1)^((1/2)+1)/3

the exponent should have simplified ((1/2)+1) -> 3/2
09-08-2016, 09:19 PM
Post: #5
 Arno K Senior Member Posts: 450 Joined: Mar 2015
RE: Different result in Integral
(09-08-2016 09:13 PM)compsystems Wrote:  (1/3)*(2*x+1)^(1/2)*(2*x+1) -> (2*x*√(2*x+1)+√(2*x+1))/3

But

[Shift]+[()]+ (1/3)*(2*x+1)^(1/2)*(2*x+1) -> (2*x+1)^((1/2)+1)/3

but with the root-symbol that does not work.
Arno
09-08-2016, 09:21 PM
Post: #6
 compsystems Senior Member Posts: 1,329 Joined: Dec 2013
RE: Different result in Integral
the CAS should have a function to replace sqrt to ^(1/2)
09-08-2016, 09:26 PM
Post: #7
 Arno K Senior Member Posts: 450 Joined: Mar 2015
RE: Different result in Integral
(09-08-2016 09:21 PM)compsystems Wrote:  the CAS should have a function to replace sqrt to ^(1/2)

Well, I often read your posts suggesting some new functions to be inserted in the Prime. I usually did not answer. Here I see the combination of the two parts to the desired result and I think most people dealing with problems like that should be able to see that, too. In my opinion some functions really are not necessary in a cas.
Arno
09-09-2016, 12:46 AM (This post was last modified: 09-09-2016 01:33 AM by compsystems.)
Post: #8
 compsystems Senior Member Posts: 1,329 Joined: Dec 2013
RE: Different result in Integral

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 =)
09-09-2016, 06:03 AM
Post: #9
 parisse Senior Member Posts: 1,190 Joined: Dec 2013
RE: Different result in Integral
I do not share your opinion compsystems, I really believe that students should learn a little bit how things work, and that includes understanding the output format of a solve command with 2 variables. Otherwise, as soon as the system was not programmed to solve their exercise, they are lost. On the other hand, the student who understands a little bit what happens can help the system solve his problem by assembling all the tools available to him. CAS are here to do the boring computing-intensive tasks, while humans are the brains that direct them.
09-09-2016, 10:34 AM
Post: #10
 jrozsas Member Posts: 158 Joined: Nov 2014
RE: Different result in Integral
(09-08-2016 08:42 PM)Arno K Wrote:  Sorry, but I tried some standard algebraic tricks on your problem and went through my list of commands for the prime to see if there is the possibility to "collect", there seems to no other possibility than looking at the result and doing it by hand.
Arno

Leo

09-09-2016, 01:43 PM (This post was last modified: 09-09-2016 03:10 PM by compsystems.)
Post: #11
 compsystems Senior Member Posts: 1,329 Joined: Dec 2013
RE: Different result in Integral
(09-09-2016 06:03 AM)parisse Wrote:  I do not share your opinion compsystems, ...

geogebra if the share with me, =) and they modify the output of commands (xCAS) to make them more similar to a "mathematical brain" artificial intelligence (AI). In talks with hpprime my students tell me. what is that output [{#, #} {#, #} , ...], with geobrebra {{x = #, y = #} ...} get the message instantly, although geogebra, also need improvement

Also think the CAS needs more simplification rules

output simplify: maximum

[Shift]+[()]+ (1/3)*(2*x+1)^(1/2)*(2*x+1) -> (2*x+1)^((1/2)+1)/3 -> (2*x+1)^(3/2)/3

((1/2)+1) - > should be simplified 3/2

Attached File(s) Thumbnail(s)

09-09-2016, 06:23 PM (This post was last modified: 09-09-2016 06:23 PM by parisse.)
Post: #12
 parisse Senior Member Posts: 1,190 Joined: Dec 2013
RE: Different result in Integral
The target audience of geogebra is not the same as the target audience of Xcas (I don't think they provide a programming language), this explains that they make different choices (and write the corresponding code).
The solve output is a good example, if you return a list of x=... y=... it's much more difficult to extract the solution if you want to do something further, for example in a script or program. The Xcas/Prime answer is much easier to reuse.
 « Next Oldest | Next Newest »

User(s) browsing this thread: 1 Guest(s)