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 giving me an bad form of the resulting expression. What am I doing wrong? Is this calculate even capable of evaluating such integrals? If not, what a waste.

Here is a photo sequence of my calculation:





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?





Even in Wolfram Mathematica, the integral is evaluated as it is in my friend's NSPIRE CX CAS (just the integral, before it is multiplied by the constant behind the integral).



HP Support Forums mentioned 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.

[Arno K]

First of all, none of the prime's answers is wrong, I simplified by hand and found them correct. Closest I get to your desired answer is a simple collect(Ans) after which you can easily see that after usage of sqrt(x)/x = 1/sqrt(x) you get exact the result from maple and ti.
Arno

[Nigel (UK)]

Your simplified result is correct. If you act on it with factor() it should be clear that it is the same as the answers on the TI Nspire and Mathematica. The only difference is that the Prime likes to write
\[1\over\sqrt{a^2+b^2}\]
as
\[\sqrt{a^2+b^2}\over a^2+b^2\]
- the root-free denominator that you referred to. I don't know how to change this behaviour.

The problem is that Simplify() doesn't know what form you want. On the Prime it tends to expand things rather than factoring them.

I hope this helps.

Also, note that the character "e" is 2.71828 to the Prime- this may cause problems if you are unaware of it. Using \(\epsilon\) from the chars menu is safer.

Nigel (UK)

[roadrunner]

Not sure if this is acceptable or desirable but with the CAS setting, simplify, set to minimum,

simplify((q*p/(4*π*ɘ*l))*∫(1/(p^2+z^2)^(3/2),z,-l/2,l/2)*√(l^2+4*p^2))/√(l^2+4*p^2)

returns almost exactly the result you want:

   

-road