integration with infinity limit has problems
07-10-2017, 01:56 AM
Post: #1
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
integration with infinity limit has problems
Whenever I try to do an integral from 0 to infinity, I seem to get an undef result and a very cryptic message.
e.g. int(e^(-a*x),x, 0,infinity)
The message is:
Undef/Unsigned Inf encountered in limit
No check were made for singular points of antiderivative -e^(-a*taylorx18)/a for definite integration in [0,infinity]

This shouldn't be a problem....what am I doing wrong?
Thx
-Donald
07-10-2017, 02:17 AM
Post: #2
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: integration with infinity limit has problems
The indefinite integral should be -(e^(-a*x))/a
For x = infinity, this becomes zero, and for x = 0, this becomes -1/a, so the answer should have been 0 - (-1/a) = 1/a
07-10-2017, 04:14 AM
Post: #3
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: integration with infinity limit has problems
I tried executing the command:
assume(a>0)
...and then I executed the integral again
....and I got one of those cryptic messages, but when I hit enter (again), it gave me the correct answer of 1/a.

What I'm running is actually this (taken from the virtual calculator)...
∫(e^((-a)*x),x,0,∞)
...interesting I just selected the formula and selected edit-copy and pasted it here, and it didn't appear exactly as on the screen, but it does show the integrate symbol.

Here is a screen capture attached below....

Attached File(s) Thumbnail(s)

07-10-2017, 04:24 AM
Post: #4
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: integration with infinity limit has problems
here is a collection of screen captures....attached below.
1. first time run assume(a>0) followed by the integral.

2. After hitting enter, the cryptic message.

3. Hitting enter again and getting the right answer of 1/a.

07-10-2017, 07:44 AM
Post: #5
 parisse Senior Member Posts: 1,090 Joined: Dec 2013
RE: integration with infinity limit has problems
The message means that the antiderivative was not checked for singularities. It is very difficult to make definite integration with boundaries for all kind of inputs, much more difficult than to compute an antiderivative, because you should make sure that the antiderivative is continuous before taking the difference at the boundaries (if there is no parameter involved, you can check against a numeric method).
07-10-2017, 10:42 AM
Post: #6
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: integration with infinity limit has problems
I've heard that this problem is common with the hp Prime, and people don't have this problem with the TI-NSPIRE or the TI89 for that matter.... So, this was a fairly simple integration problem. It shouldn't have required anything complicated.
Is there something I can tell it before giving it the integral to calculate to avoid this message, like something inside the assume() function? How can I tell the system that the function is continuous or whatever it needs to know to do the calculation. I mean if I were to do this manually, I wouldn't need anything like this.....the calculator should be able to do the same thing as me doing it manually.
If you know how, please give me the steps to type if I wanted to simply calculate
int(e^(-a*x),x,0,infinity)
07-10-2017, 11:43 AM
Post: #7
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: integration with infinity limit has problems
FYI, I also tried assume(a,integer); additionally(a>0);
still got the message.
I was able to use wolfram alpha and didn't have to do anything weird and it gave me the right answer. Like I said, other online forums have said that TI89 and TI-NSPIRE don't seem to have this problem either.
Seems like it's only in the hp prime...
If only I knew what I needed to type in an assume statement or something to achieve the checks it's talking about in the cryptic message.
07-11-2017, 12:11 PM
Post: #8
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: integration with infinity limit has problems
I put in a new post to help people that encounter these problems in the future here...
07-15-2017, 08:36 PM
Post: #9
 Tim Wessman Senior Member Posts: 2,228 Joined: Dec 2013
RE: integration with infinity limit has problems
As you've noticed, the CAS is quite verbose. It likes to tell you, the user, anything that might help you understand the results instead of simply returning "an answer". The nspire tucks information like "hey, this might not be correct in all domains" and similar types of warnings under an additional warning icon you need to click.

The CAS author really feels like that information should be presented immediately to let the (now informed) user understand. In most cases, just ignoring the extra information about what the CAS was doing as you noted matches the results you get elsewhere.

That being said, I'd like to tuck the additional CAS messages away under another little information icon next to each result or something to avoid causing confusion like this.

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
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