Strange value returned by solve()

[Fred Nurk]

I typed in solve(integral(3 / (x - k) dx x = 3...5), k) and k = 2 or k
= 7 / 2 was returned. Then when I entered integral(3 / (x - 7 / 2) dx)
I get undef.

When I solved for k by hand, I only got k = 2. How does one explain
this?

TIA,
Fred

[Nelson Sousa]

I don't quite understand the command you just entered. You have 3...5, what's missing in between? Can you type the exact command?

About the double solution displayed, being that one of those is a real solution: did you get a warning message? Sometimes the Nspire CAS returns a warning message saying "The domain of the result might be higher than the domain of the input", which means that some displayed values might not be actual solutions of the problem.

Example: solve( (x-1)(x+2)^2/(x+2) = 0 , x) will return x=1 or x=-2. But x=-2 is not in the domain of the LHS, so it's not a solution of the original equation. When solving by hand you get (x-1)(x+2) by simplification, but you must be aware that the domain of the original problem is R / {-2}.

Cheers,

Nelson

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[AdRiWeB]

By 3...5 I think he meant the integral from 3 to 5.

On 26 juil, 11:13, Nelson Sousa <nso...@gmail.com> wrote:
> I don't quite understand the command you just entered. You have 3...5,
> what's missing in between? Can you type the exact command?
>
> About the double solution displayed, being that one of those is a real
> solution: did you get a warning message? Sometimes the Nspire CAS returns a
> warning message saying "The domain of the result might be higher than the
> domain of the input", which means that some displayed values might not be
> actual solutions of the problem.
>
> Example: solve( (x-1)(x+2)^2/(x+2) = 0 , x) will return x=1 or x=-2. But
> x=-2 is not in the domain of the LHS, so it's not a solution of the original
> equation. When solving by hand you get (x-1)(x+2) by simplification, but you
> must be aware that the domain of the original problem is R / {-2}.
>
> Cheers,
> Nelson
>

> On Mon, Jul 26, 2010 at 07:51, Fred Nurk <albert.xtheunkno...@gmail.com>wrote:
>
> > I typed in solve(integral(3 / (x - k) dx x = 3...5), k) and k = 2 or k
> > = 7 / 2 was returned. Then when I entered integral(3 / (x - 7 / 2) dx)
> > I get undef.
>
> > When I solved for k by hand, I only got k = 2. How does one explain
> > this?
>
> > TIA,
> > Fred
>
> > --
> > To post to this group, send email to tins...@googlegroups.com

> > To unsubscribe send email to tinspire+u...@googlegroups.com<tinspire%2Bunsu...@googlegroups.com>

[John Hanna]

Solve requires an equation, like

          Solve(2x+3=7,x)

 

Your text: solve(integral(3 / (x - k) dx x = 3...5), k)

doesn't look like an equation to me.

 

Something's missing, Fred.

 

John Hanna

jeh...@optonline.net

www.johnhanna.us   

T³ - Teachers Teaching with Technology

"Reality is an approximation."

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[Fred Nurk]

Nelson Sousa wrote:
> I don't quite understand the command you just entered. You have 3...5,
> what's missing in between?

I mean the definite integral from x = 3 to x = 5.

> About the double solution displayed, being that one of those is a real
> solution: did you get a warning message? Sometimes the Nspire CAS returns a
> warning message saying "The domain of the result might be higher than the
> domain of the input", which means that some displayed values might not be
> actual solutions of the problem.

No, I didn't.

Note: I left out that the definite integral = 3 * ln(3). Sorry.

Fred Nurk.

[Nelson Sousa]

The problem here is that the undefined integral is

-3* ln( abs(k-3) / (k-5) ).

If you equal this to 3*ln(3) you get in fact two different solutions, k=2 and k=7/2 ( you can manually check this).

The issue here is that k=7/2 makes the function to be integrated to have a singularity in the interval [3,5], so the integral is not well defined.

When solving equations if more solutions are displayed, there's usually a warning saying that the domain of the result may be larger than the domain of the original expression, example:

solve( (x+1) * (x+2)^2 / (x+2) =0,x)

will return two solutions, x=-1 or x=-2, but x=-2 is not part of the domain.

But when the integral is computed, the resulting expression doesn't know about the interval of integration nor about the types of singularities in the function, so doesn't detect it.

When dealing with this kind of problems it's advisable to do the problem by pieces, one step at a time and then checking whether the solutions make sense. These situations may arise with any CAS system (they know how to simplify, but fomr some things you still need a human being looking at the results and interpreting them).

Cheers,

Nelson

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