Can't Evaluate Integral (Electromagnetic Fields & Wave Integral)

[Carl_Doverman]

I can't evaluate the following integral. This is an integral commonly used in electromagnetic field theory. 1/4piE is the proportionality constant and P is the charge density. I am integrating this expression with respect to Z. One of my friends with an NSPIRE CX CAS evaluated this integral with ease, giving him an accurate resultant expression. My HP Prime is refusing to calculate the given integral and it instead just throws me an error, seen in the lower right image. What am I doing wrong? Is this calculate even capable of evaluating such integrals? If not, what a waste.

[Joe_Horn]

There are several problems with your input syntax which are causing Prime trouble:

(1) Uppercase single-letter variables in Prime always have real number values. They cannot be used as formal variables in CAS. Be sure to change all the variables to lower-case letters, and be sure that they are not already assigned a value.  If necessary, you can type the CAS command "restart" which deletes ALL existing CAS variables and resets the CAS settings.

(2) Prime doesn't like implied multiplication.  So be sure to insert the missing multiplication symbol between the fraction and the integral symbol.

(3) It's best not to use "e" as a variable because it is a system constant (Euler's Constant).  If a formula contains a variable called "e" which is not Euler's Constant, you should use some other name for it in your Prime.

After making those changes to your input, Prime will understand it and work with it correctly.  Depending on your current CAS Setting for Simplification, you may need to tap the [simpilfy] menu button to simplify the result.

Hope this helps!  Disclaimer: I don't work for HP, but I enjoy using their calculators.

[Carl_Doverman]

I did as you suggested and got a result. However, it is not correct. Here are the steps that I took in photo sequence:

This simplified final result is pretty wrong. My friend got the accurate answer on his NSPIRE CS CAX...here is his screen. P.S. Using reserved variables didn't affect his calculation, he said. Using other variables in my calculation made no difference, only asterisks and parentheses. Regardless of this, I cannot get his result. Help?

[calcpeace]

Hello  Carl,

Hp prime is right, too, but it gave you the answer with a fraction where the denomiator is root-free. 

q/(2*p*pi*e*sqrt(l^2 + 4*p^2)) =  (q*sqrt(l^2 + 4*p^2))/(2*p*pi*e*(l^2+4*p^2))

Sincerely calcpeace!

[Carl_Doverman]

Even in Wolfram Mathematica, the integral is evaluated as it is in my friend's NSPIRE CX CAS.

You mention it's denominator is root-free (the HP Prime's calculation), how do I change this? How do I make it so I receive the same result as my friend and Mathematica? Thank you.

[calcpeace]

Hello Carl,

I don't owe a prime, but maybe this discussion helps you more in this philosophical topic (in my point of view). 

HERE! 

Sincerely calcpeace

[Maké]

Hi!, @Carl_Doverman:

Welcome, to HP Forum !. 

If you needed, Gauss Law ... http://www.maxwells-equations.com/gauss/law.php

In the HP PRIME, you can use this Eddie Shore programm, from ... http://edspi31415.blogspot.com.ar/2015/04/hp-prime-electric-field-flux-gausss-law.html

[Carl_Doverman]

According to what's written there, I should be using the collect() command, which I have..with no intended results. The sqrt() term remains in the numerator. Which commands should I follow in order to take my result from it's current form to my friend's and Mathematica's form? I'm sorry for re-stating my question but the article you replied with didn't really help me..

[calcpeace]

Hello Carl,

I'm afraid there is no advice for your problem, it is a general decision in CAS what does "simplify" mean.

The hp 50g has a "MATCH" command (maybe the Prime, too), with this you can implement your own rules how to transform algebraic terms.

I tried this with my hp 50g and it works! Thank you for sharing your problem, so I learned something more about the power of my calc.

Sincerely peacecalc

[Tim_Wessman]

Hello,

Can you please have your friend try the definite integral of ln(x)*sin(x) and report report what they discover? Why does the CAS in Prime give a result that the TI *cannot*? (you can only get an approximation, not an actual definite integral)

https://www.wolframalpha.com/input/?i=integral+ln(x)*sin(x)

The point here is that CAS systems have different capabilities and methods of operation. The CAS in the Prime is unquesitonably more powerful the the one in the TI calcs, but that does not mean that every CAS will return identical results or do things using identical algorithmns, or even have identical capabilites. TI has primarily tuned the CAS to give "nice" looking answer for many types of lower level math operations such as high school calculus/AP type calculations, but complelely excluded more advanced features you need in upper level courses.

It is just a matter of differing priorities and focus.

A mathematical result being in a different form isn't "incorrect", but some systems might put things in a form that you prefer over another. In this case, the CAS in prime follows the convention that "simplest" means no radicals in the denominator and there really isn't a simple way to "undo" that.