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Integration function on the 50g?
Message #1 Posted by Hal Bitton on 11 June 2007, 5:44 p.m.

Hi everybody. I'm having trouble figuring out to symbolicly evaluate and display the integral of a function on my 50G.
Consider the very simple expression: F(x)=x^2.

On my 48gx I simply choose "integrate" from the symbolic menu, which brings up a wonderful (and simple) form where I can enter my function (in this case x^2) and the upper and lower limits of evaluation. I am also presented with the option of choosing a symbolic or numeric answer. If I choose the symbolic option and run the integration, I get the symbolic solution in level 1 of the stack. Within this solution, the integral of my function (in this case x^(2+1)/(2+1) ) is clearly visable.

After pouring through the 50G users guide, I can find no such functionality on the 50G. I can get a numeric result by keying the integral into the equation writer, and then evaluating it, but a symbolic solution continues to elude me. I have "step by step" checked in the CAS options.

So in short my question is this: On the 50G how can I integrate the function x^2, and see somewhere in the solution the symbolic integral of this function, namely x^(2+1)/(2+1) ?

Any help from you 49/50 series experts out there would be much appreciated.
Thanks and best regards, Hal

      
Re: Integration function on the 50g?
Message #2 Posted by Gene on 11 June 2007, 5:57 p.m.,
in response to message #1 by Hal Bitton

Check the learning modules for the 50g on the 50g webpage.

You can do this in the Equationwriter application for instance.

Key X^2, then select it.

Choosing INTVX will integrate it to X^3/3.

You can do this in the stack the same way, depending somewhat on your flag settings.

Look here:

http://h20331.www2.hp.com/Hpsub/downloads/50gSymbolic_integration_of_polynomials.pdf

Good luck, Gene

            
Re: Integration function on the 50g?
Message #3 Posted by Hal Bitton on 11 June 2007, 6:18 p.m.,
in response to message #2 by Gene

Thanks for your responce, Gene.
When I key x^2 into the equation writer and then choose INTVX, I get INTVX(x^2) displayed in the equation writer. Any attempts to evaluate it (whether in the equation writer or on the stack) gives me the goofy result:

x^2
rational fraction
x^2

displayed in the equation writer. I have no idea how to interpret this.
What do you suppose I'm doing wrong?
Thanks again, Hal

      
Re: Integration function on the 50g?
Message #4 Posted by Massimo A. Santin on 11 June 2007, 6:07 p.m.,
in response to message #1 by Hal Bitton

Quote:
So in short my question is this: On the 50G how can I integrate the function x^2, and see somewhere in the solution the symbolic integral of this function, namely x^(2+1)/(2+1) ?

Using INTVX (not in approx mode). Using RPN mode

'X^2' ENTER INTVX ENTER

or using algebraic mode

INTVX('X^2')

INTVX is in CALC/DERIV & INTEG. menu but you can use SYMB, CALCULUS, INTVX.

            
Re: Integration function on the 50g?
Message #5 Posted by Hal Bitton on 11 June 2007, 6:33 p.m.,
in response to message #4 by Massimo A. Santin

Thanks very much, Massimo.
That worked. It seems I was stopping one (ENTER) keystroke to soon. Still the intermediary result "x^2 rational fraction x^2" puzzles me, but at last now I can get the predicted and correct end result.
While I've got you one more question if I may...the user's guide speaks of the function INT, which will let me evaluate an integral for any variable, not just the default CAS variable. I can't seem to find this function, however. Is it called something else in the softkey labels?
Best regards, Hal

                  
Re: 50g Integration
Message #6 Posted by Happy HP User on 12 June 2007, 12:18 a.m.,
in response to message #5 by Hal Bitton

To symbolically integrate with regards to variables other than X, such as s,t,x... use the RISCH command, which uses a partial implementation of the Risch algorithm, example:

2: COS(t)

1: 't'

RISCH

1: SIN(t)

                        
Re: 50g Integration
Message #7 Posted by Hal Bitton on 12 June 2007, 2:29 a.m.,
in response to message #6 by Happy HP User

Worked like a charm.
Once again, thanks very much.
Hal

                              
Re: 50g Integration
Message #8 Posted by Norris on 12 June 2007, 6:54 p.m.,
in response to message #7 by Hal Bitton

Quote:
Still the intermediary result "x^2 rational fraction x^2" puzzles me
If you uncheck the "Step/Step" option in MODE CAS, then

'X^2'
ENTER
INTVX

should return:

1/3 x X^3

immediately, without the message.

RISCH works like INTVX, except that you have to specify the independent variable; it doesn't look for one in VX, e.g.

'Y^2'
ENTER
'Y'
ENTER
RISCH

                                    
Re: 50g Integration
Message #9 Posted by Ron Allen (Fairhope) on 12 June 2007, 11:58 p.m.,
in response to message #8 by Norris

The "rational fraction" method is the method used for integrating x^2dx. try integrating 1/cos(x) using the free x with CAS. keep the step-by=step on and watch the messages for those interim solutions, like "trig substitution u = sin(x)," etc. For this solution with notice of steps, i.e., full info, do the following.

I call this the "Show your work, student" method turn on the EQW to write the equation, use back cursor arrow to select and highlight the entire equation, press left shift (white), then CALC (under the 4), press 6 to highlight INTVX AND OK. CUE on the menu line looing for the ok isolated bottom left of the screen and press ok when it presents itself, alternately press EVAL when ok is crowded out of the menu. When there remains no further improvement, ENTER and the stack will hold all of the steps it recorded in process, assuming that's what you want. If the final answer is all you want, follow the other's instructions. By pressing the one line clear you can read off the evolution of the process in reverse.

1/cos(x) integrated has at least three solutions with the same final result. There are ways to get the symbolic results with or without the notes, even the old 48gx way setting the parameters of integration to 0 through x which forces the symbolic solution.

The notes of various methods include trig substitution with "u = something, too bad they don't give you du and f(u) modified after the u is extracted, but I guess you can't have it all, rational fractions, partial fractions, integration by parts, even plain old antiderivatives, etc. The point is, you can use this powerful feature to give up or hide all or none of the work and present you what you want, even numericals. I have yet to fail to integrate an equation, which doesn't mean there aren't any, I just haven't run across one in the normal course.

Keep trying,

Ron

                                          
Re: 50g Integration (errata)
Message #10 Posted by Ron Allen (Fairhope) on 13 June 2007, 1:31 p.m.,
in response to message #9 by Ron Allen (Fairhope)

Sorry for the inconvenience, but the system won't allow the editing of the previous message, so this errata.

In the original I refer to the "ok" at the bottom left of screen - should be right instead of left.

In the original I refer to the extraction of "u" meant "du"

apologies,

Ron

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