Post Reply 
Set parameter bounds for improper integral
07-22-2021, 06:32 AM (This post was last modified: 07-22-2021 08:30 AM by carey.)
Post: #1
Set parameter bounds for improper integral
I tried integrating e^(-s*t) dt between 0 and infinity where s>0, so I set up the integral and used the "where" operator | to set s>0. The correct answer is 1/s but I get syntax errors on my Prime and in the emulator.

The prime emulator screenshots show (i) Home screen attempt; (ii) CAS screen attempt (input); (iii) CAS screen attempt (output).

Thanks for any suggestions!
           

UPDATE:

The correct answer of 1/s can be obtained by typing on the CAS screen:

integrate(e^-s*t,t,0,+infinity)|s>0

After a warning message the Prime displays a pretty printed integral with the correct result.

Screenshots of the CAS input and output in the emulator are attached.

       

Is there a way to obtain the correct result using the integration template?
Find all posts by this user
Quote this message in a reply
07-22-2021, 09:04 AM
Post: #2
RE: Set parameter bounds for improper integral
You are probably putting t|s>0 on accident. Make sure you move one space right to get out of the d(t) part... you have d(t|s>0) not d(t)|s>0...

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
Find all posts by this user
Quote this message in a reply
07-22-2021, 09:52 AM (This post was last modified: 07-22-2021 09:55 AM by carey.)
Post: #3
RE: Set parameter bounds for improper integral
Thanks Tim for your help!

If you are referring to the 3rd screenshot, it shows the CAS output that displays after clicking Enter from the CAS input (screenshot 2) where there is a space separation after the dt. (I'm curious why the CAS output doesn't seem to reflect what was entered in the CAS input template but will save that question for another time).

I'm sure I am making some silly syntax error but am still at a loss as to what it is.

Thanks again!
Find all posts by this user
Quote this message in a reply
07-22-2021, 10:55 AM
Post: #4
RE: Set parameter bounds for improper integral
Algebraic entry is my default setting. What you type is what you get.

CAS> assume(s > 0)
CAS> integrate(e^(-s*t),t,0,inf)       → 1/s
Find all posts by this user
Quote this message in a reply
07-22-2021, 02:41 PM
Post: #5
RE: Set parameter bounds for improper integral
Perfect! That did the trick!

Thanks Albert!
Find all posts by this user
Quote this message in a reply
07-27-2021, 01:29 AM
Post: #6
RE: Set parameter bounds for improper integral
(07-22-2021 09:04 AM)Tim Wessman Wrote:  You are probably putting t|s>0 on accident. Make sure you move one space right to get out of the d(t) part... you have d(t|s>0) not d(t)|s>0...

I've seen students get hung up with this issue numerous times, usually with some arithmetic operation. So instead of

∫x²dx +5 ie, ∫(x^2,x)+5

they enter

∫x²dx+5 ie, ∫(x^2,x+5)

The error is very subtle visually in Textbook mode. You'd only notice it if you knew to look for it.

The Nspire handles this by surrounding the term with parentheses whenever the expression is anything more than a single variable. So the above error looks like

∫x²d(x+5)

which clearly shows the user what is really happening.

Is there any way to get the template to do something similar? As it is, the error message tells the student that something has gone wrong, but there is no indication of what the source of the error is. The student is at a loss trying to figure out what went wrong.
Find all posts by this user
Quote this message in a reply
07-27-2021, 01:20 PM
Post: #7
RE: Set parameter bounds for improper integral
(07-27-2021 01:29 AM)Wes Loewer Wrote:  So instead of

∫x²dx +5 ie, ∫(x^2,x)+5

they enter

∫x²dx+5 ie, ∫(x^2,x+5)

The error is very subtle visually in Textbook mode. You'd only notice it if you knew to look for it.

Both had "∫x²dx+5" in CAS input history ... not just subtle, but identical Sad

Since CAS does not support ∫x² d(x+5) = x³/3 + C, why should the space be necessary ?
Both should have parsed as ∫(x^2,x) + 5
Find all posts by this user
Quote this message in a reply
Post Reply 




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