Integral problem

[Jim Fullerenex]

Here is a simple integral :

∫sqrt( 2(1-cos(t)) ) dt

The answer is even simpler: -4cos(t/2) by a basic trig identity.

But the CAS doesn't seem able to handle it, even when I also asked for the answer of a definite integral (t from 0 to 2pi) instead of the indefinite one.

I tried to constrain the domain of t, and even added tExpand() and tCollect, but nothing helped. The answer is misleading, just like the tangent integral problem I posted earlier.

Calculus BC teachers, please say something. Shall we consider it a bug that must be fixed right away? Or is it also beyond the scope of high school?

Best,

Jim

[Dennis Donovan]

Trig Substitution method of integration is not tested on the BC exam.  So in that sense, it is beyond the cope of HS.

I tried  two definite integrals (including [0, 2pi]) and that worked as far as I can tell.  (screen shot)

Dennis Donovan

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From: Jim Fullerenex <smoa...@gmail.com>
To: Nspire Group <tins...@googlegroups.com>
Sent: Saturday, April 7, 2012 11:30 PM
Subject: [tinspire] Integral problem

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[Jim Fullerenex]

The answers in the screenshot are NOT exact solutions. And in approximate mode, EVERY integral can return a numeric answer. So the CAS still fails.

Even if the basic trig substitutions are not required in AP, they are still taught in quite a number of high school enrichment courses. It's so simple that a CAS (a computer) should be able to do. Lots of integrals that Nspire can do go well beyond our imagination, but for this one, oops.

*The answer will very likely mislead students (and has already misled a little friend of mine) into assuming that the integral of sqrt(2(1-cos(t)) is algebraically inexpressible.

Maybe it's better to send a report to TI (which is the point I'm trying to make) than to give an excuse by arbitrarily limiting the scope of HS.

Best,

Jim

2012/4/8 Dennis Donovan <ddh...@yahoo.com>

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[Dennis Donovan]

> Maybe it's better to send a report to TI (which is the point I'm trying to make) than to give an excuse by arbitrarily limiting the scope of HS.

Your question was is this beyond the scope of HS in the context of BC Calculus, and the answer to that question is yes (in that context).  I know that trig sub is taught in many HS courses, but that was not your question.  Don't tell me I'm making excuses by answering a question YOU asked.

Bottom line is that if it's a bug,. it needs to be fixed, I don't know why you need to solicit opinions on whether it is a bug that the CAS won't perform a certain integral ... if it can't perform the integration, then it is a bug, period.

---

From: Jim Fullerenex <smoa...@gmail.com>

To: tins...@googlegroups.com
Sent: Sunday, April 8, 2012 2:21 AM
Subject: Re: [tinspire] Integral problem

[Joe]

May I respectfully suggest that you call TI-cares about the bug and
then let us know if they actually care. I would be pleasantly
surprised if they did anything about it. I seem to recall that the
cas doesn't recognize some trig identities and that has been known for
many years.

On Apr 7, 11:21 pm, Jim Fullerenex <smoat...@gmail.com> wrote:
> The answers in the screenshot are NOT exact solutions. And in approximate
> mode, EVERY integral can return a numeric answer. So the CAS still fails.
>

> Even if the *basic* trig substitutions are not required in AP, they are

> still taught in quite a number of high school enrichment courses. It's so
> simple that a CAS (a computer) should be able to do. Lots of integrals that
> Nspire can do go well beyond our imagination, but for this one, oops.
>
> *The answer will very likely mislead students (and has already misled a
> little friend of mine) into assuming that the integral of sqrt(2(1-cos(t))
> is algebraically inexpressible.
>
> Maybe it's better to send a report to TI (which is the point I'm trying to
> make) than to give an excuse by arbitrarily limiting the scope of HS.
>
> Best,
> Jim
>

> 2012/4/8 Dennis Donovan <ddha...@yahoo.com>

>
>
>
>
>
>
>
>
>
> > Trig Substitution method of integration is not tested on the BC exam.  So
> > in that sense, it is beyond the cope of HS.
>
> > I tried  two definite integrals (including [0, 2pi]) and that worked as
> > far as I can tell.  (screen shot)
>
> > Dennis Donovan
>

> >   ------------------------------
> > *From:* Jim Fullerenex <smoat...@gmail.com>
> > *To:* Nspire Group <tins...@googlegroups.com>
> > *Sent:* Saturday, April 7, 2012 11:30 PM
> > *Subject:* [tinspire] Integral problem

>
> > Here is a simple integral :
>
> > ∫sqrt( 2(1-cos(t)) ) dt
>
> > The answer is even simpler: -4cos(t/2) by a basic trig identity.
>
> > But the CAS doesn't seem able to handle it, even when I also asked for the
> > answer of a definite integral (t from 0 to 2pi) instead of the indefinite
> > one.
>
> > I tried to constrain the domain of t, and even added tExpand() and
> > tCollect, but nothing helped. The answer is misleading, just like the
> > tangent integral problem I posted earlier.
>
> > Calculus BC teachers, please say something. Shall we consider it a bug
> > that must be fixed right away? Or is it also beyond the scope of high
> > school?
>
> > Best,
>
> > Jim
>
> > --
> > To post to this group, send email to tins...@googlegroups.com

> > To unsubscribe send email to tinspire+u...@googlegroups.com
> > For more options, visit this group at
> >http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
> > The tns documents shared by group members are archived at
>

> >https://sites.google.com/site/tinspiregroup/classroom-news/welcome-ab...

>
> >    --
> > To post to this group, send email to tins...@googlegroups.com
> > To unsubscribe send email to tinspire+u...@googlegroups.com
> > For more options, visit this group at
> >http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
> > The tns documents shared by group members are archived at
>

> >https://sites.google.com/site/tinspiregroup/classroom-news/welcome-ab...

[Jim Fullerenex]

There's a little misunderstanding here. Actually the question is more rhetorical than literal.

The main purpose of this post is to ask more people to tell TI-Cares. One person never makes any difference.

I'm asking for (and expecting) more support from the members here, and I'm justifying this support on the ground that this class of trouble falls in the scope of the good old "target group". period.

Best,

Jim

[Nevil Hopley]

Jim recently posted the comment:

"The main purpose of this post is to ask more people to tell TI-Cares. One person never makes any difference."

I would like to offer an alternative viewpoint on items that are posted in this forum, and communicated to TI by other means.

1. There are TI employees who monitor this forum and pick up all relevant points.

An example of one of them 'breaking cover' was here, from back in September 2011....

https://groups.google.com/forum/?fromgroups#!searchin/tinspire/tysun/tinspire/AzOxF8iHuKk/NC40wOllDdMJ

2. I am of the opinion that one person can make a difference. I know of several developments and improvements that have been made to the TI Nspire operating system and computer software that have come directly from one person's request, without having to flood TI-Cares with a wave of the same requests.

So, I guess I just reminding everyone that this forum can be as good a place (if not better?) than sending a request into TI-Cares, as the TI employees can see the whole thread of a discussion and see where the original request came from, and how important it is to some people.

Nevil

PS I also had the pleasure of meeting some of the CAS engine design team at Chicago back in March 2012 and I acquired a small insight into the challenges they face in keeping the CAS code optimal, and functional, whilst running it on a handheld device with both finite memory and processing power. Their timeline for development and bug-testing of new or 'fixed' features is not an overnight process either. They don't want to fix one thing if it causes another thing to break as a consequence.

[Joe]

On Apr 9, 5:54 am, Nevil Hopley <ne...@calculatorsoftware.co.uk>
wrote:

> . They don't want to fix
> one thing if it causes another thing to break as a consequence.

Ha,ha,haha. I'm old and gray and I thought I had heard all the
excuses there for not doing a job and doing it right. The solution to
not being able to fix something without causing another thing to break
is to replace the people who can't the job correctly with people who
can. And BTW the solution to fixing bugs in a timely manner is also to
hire people who can and enough of them.
When I was young and foolish I once made the mistake of telling a boss
that "I don't think I can do what you want done." His reply was "if
you can't do the job, I'll get some one who can." I never used that
excuse again. Ever.

[Eric Findlay]

Joe,

You have said previously that you do not have programming experience. I would like to let you know that it is not as simple as "to hire people who can and enough of them." working with any decent sized piece of code is tricky enough, but when you start working with super complex jobs like operating systems or CAS, where so many pieces of code are used by so many other parts of the program, and where different parts of the system were written by several different people, you bet it's easy to accidentally "break" something while fixing a bug. I don't know a programmer who hasn't done this. I've done it several times myself. It's not a matter of laziness or insecurity or incompetence, by merely a fact of working with a complicated system designed in parts by many people. I appreciate the time they put into trying to reduce this, but if you recall a couple OS versions ago, sometimes these correction-caused new bugs do slip through. By taking more time to fix and test these bugs, they are doing their job and doing it right. It just might not be at a speed of your liking, but it's being done right.

Also, it's not even as simple as "fixing the bug." Sometimes it's very, very difficult to find out where the error is coming from, or what is causing the problem. And once you find it, if it's in a common piece of code, you then have to strategize the best method of fixing or replacing the problem. Sometimes this may mean a complete rewrite of a function in order to satisfy the rest of the functions that depend on it.

Please do not write off their jobs as simple, or imply they are incompetent. They are human and do make mistakes, but they are professionals and are doing it right.

--Eric

[Jim Fullerenex]

Thank you Nevil! I surely hope if my request (whether it's improvement suggestion or bug report) is reasonable enough, I alone can make a difference (judging from earlier posts, some people tend to misunderstand anyway).

FYI, I was contacted by a personnel (for the very first time) shortly after I posted the trig integral problem. I'm very happy about that.

Best,

Jim

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