# Nspire cx CAS - Laplace inverse fails

I'm trying to calculate that easy integral but I get undef. When I replaced $\infty$ with $1000$, I got the right answer. ($e^{-1000}$ is zero roughly). Although this calculator knows that $e^{-\infty} = 0$ (as you can see).

What's the problem?

(I know that there is many programs that can get Laplace transformation easily... I'm trying to fix this issue.)

EDIT:

Well, it worked when I replaced $s$ with $5$. Isn't there any way to make assumptions? Or storing a number as a variable and getting the answer in terms of it somehow...

EDIT2:

It worked with a little trick :D I used the number $e$ or $\pi$ to get the answer in terms of them

• Does the calculator know you're assuming $s > 0$? It can't read your mind. Dec 26, 2014 at 8:06
• Dear users: instead of flagging this as "low quality", comment and tell the OP how he can improve his post.
– Pedro
Dec 26, 2014 at 8:13
• Your trick with magic numbers $e$ and $\pi$ is dangerous: you could get the answer which could have more instances of them, and then simplification and replacing them with $s$ would give you the wrong answer. Instead I'd try using essentially positive $s$, like $m^2$ (if your calculator doesn't assume the variables to be complex) or even just $|s|$. Dec 26, 2014 at 12:49
• Or, if it doesn't assume $s\ne0$, then use something like $|p|+1=s$, so that $s>0$ strictly. Dec 26, 2014 at 12:57
• Nothing of that even worked.. I don't get it, how using magic numbers could lead to a wrong answer?! if it's s^2 then it'll be e^2... can you explain with an example? Thanks for your concern :) Dec 27, 2014 at 12:13

It's an old question but the answer might help someone :

In fact you just have to define $$s$$ as $$s>0$$ with the '|' symbol, like this (screenshot in the link) : Usage of the '|' symbol to define assumption for $$s$$

You can use '|' whenever you have to specify an assumption to the calculator.

• I knew this long time ago but I totally forgot about this question. Thanks, this might be useful to someone else. Jun 29, 2017 at 19:12

I can't be 100% sure that this is why your calculator is doing this, but here is a possibility:

The integral $\displaystyle\int_{0}^{\infty}e^{-st}\,dt$ converges to $\dfrac{1}{s}$ only if $\text{Re}[s] > 0$.

However, the integral $\displaystyle\int_{0}^{1000}e^{-st}\,dt$ equals $\dfrac{1}{s} - \dfrac{e^{-1000s}}{s}$ for any value of $s$ except $0$.

If the calculator made the assumption that $s \neq 0$ but doesn't know to assume $\text{Re}[s] > 0$, then it might think the first integral isn't defined, while correctly outputting the value for the 2nd integral.

• I edited the question, it worked when I replaced s with 5 or any number. I'll try to look for how to make assumptions or use symbols instead of numbers. Appreciated :) Dec 26, 2014 at 8:17

Try this program, It's for the TI nspire cx cas it does Laplace & inverse Laplace including the Dirac (impulse) and Heaviside step functions. the instructions are in French. You can always use google to translate the info. http://seg-apps.etsmtl.ca/nspire/enseignement/ETS_specfunc.tns