Integration results puzzle

[KeithB]

I have been working with some RC decay problems, so have been using my Prime.

(Sorry, I don't know how to enter equations.)

I used the CAS to integrate e^-x from 0 to 5.

I get an answer something like exp(-1/5 + 1)

I copy this to the command line, hit home and enter and get the result .99326... which is what I expect.

When I use the e^x button and enter the exponent: +/-, 1,/,5,+,1 and hit enter I get 2.2255

when I calculate e^x with an exponent of 4/5, I get a result of 2.2255

What is the difference?
The only difference I see, and it is real subtle, is that for the correct case the 5 is centered under the divide bar and for the incorrect case the 5 is right justified.

[DA74254]

Use the 3rd white key (to the right for the toolbox key).
Here you'll find the integration template.

Then, there's just to plug in the numbers. "x" is on the key right of the template key you just used..
But you have to hit the +/- key before the "x" key in order to get the desired result.

[KeithB]

(02-18-2019 03:17 PM)DA74254 Wrote:  Use the 3rd white key (to the right for the toolbox key).
Here you'll find the integration template.

Then, there's just to plug in the numbers. "x" is on the key right of the template key you just used..
But you have to hit the +/- key before the "x" key in order to get the desired result.

I entered the integral just fine, I meant I could not get a pretty equation on the forum here.

[DA74254]

Ah, OK.
Then, I might not be the right person to help you

[DrD]

It's not real clear in the prime's display, but you are working with two different exponents:

(-1/e^5)+1 approx 0.9932 ... isn't the same as e^((-1/5)+1) approx 2.2255 ...

That's a distinction WITH a difference! If you copy/paste those into the command line, they do (sort of) look the same.

[mfleming]

If you evaluate the integral in CAS, switch to Home and then do a View/Copy From CAS to get the result, you can compare the difference between it and your hand entry of the result. Evaluating the copied result gives you what you'd expect. I'll leave it to someone more knowledgable with the Prime to explain the difference between that and your hand entry!

~Mark

[KeithB]

(02-18-2019 03:37 PM)DrD Wrote:  It's not real clear in the prime's display, but you are working with two different exponents:

(-1/e^5)+1 approx 0.9932 ... isn't the same as e^((-1/5)+1) approx 2.2255 ...

That's a distinction WITH a difference! If you copy/paste those into the command line, they do (sort of) look the same.

exactly:
So why does the 1 look like part of the exponent?

[KeithB]

I played around with it last night, and boy, is it a subtle difference, but it is there.

It did not help that I got temporarily confused and thought that e^1/5 was 1/e^5 and not the fifth root of e. grrr.

[DrD]

I believe the authors are aware of this display confusion, so we will have to wait for a possible future update to correct it.

[mfleming]

Interestingly, if the equation is entered as 1+(-1/e^5) the formatting confusion vanishes. I guess the eye is drawn to the e on the bottom and falsely concludes the rest of the expression is the exponent. So much for the naturalness of Textbook mode!

~Mark