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
 carey Junior Member Posts: 21 Joined: Feb 2014
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?
07-22-2021, 09:04 AM
Post: #2
 Tim Wessman Senior Member Posts: 2,277 Joined: Dec 2013
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.
07-22-2021, 09:52 AM (This post was last modified: 07-22-2021 09:55 AM by carey.)
Post: #3
 carey Junior Member Posts: 21 Joined: Feb 2014
RE: Set parameter bounds for improper integral

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!
07-22-2021, 10:55 AM
Post: #4
 Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
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
07-22-2021, 02:41 PM
Post: #5
 carey Junior Member Posts: 21 Joined: Feb 2014
RE: Set parameter bounds for improper integral
Perfect! That did the trick!

Thanks Albert!
07-27-2021, 01:29 AM
Post: #6
 Wes Loewer Senior Member Posts: 344 Joined: Jan 2014
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.
07-27-2021, 01:20 PM
Post: #7
 Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
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

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
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