Differential Length (Cylindrical Coordinates)

[salman213]

So we just were given some formulas and I am confused about this simple question

Find the differential length or distance between the two points.

P(2,pi/2,-1) and Q(5,3pi/2,5)I know this

for cylindrical

dL = dp (ap) + p dphi (aphi) + dz (az)

So i would integrate

I have a few questions does it matter if for example for dp

i integrate from 2 to 5 or from 5 to 2?

also in the aphi part, there is a "p" which is not constant in my problem so how can i do the integral with respect to dphi when p is not constant!

can I even use this?

helpEDITED: MY TEXT USES A DIFFERENT NOTATION I POSTED ANOTHER QUESTION AND THE INDIVIDUAL ALSO HAD PROBLEMS WITH MY NOTATION I HOPE THIS DIAGRAM HELPS IT'S FROM MY TEXTBOOK:

http://img261.imageshack.us/img261/7998/53164335jl9.jpg

 

[Gib Z]

I am a bit confused as to your notation but;

It does matter which order you integrate from. By convention length must be a positive quantity and so our integral must output positive values. Choosing the integral with upper limit of integration as 5, and lower limit as 2, we achieve that, but if we were to do it the other way around, the value we would get is negative.

Also, I'm a bit confused as to what specifically you are talking about, but if the integral is with respect to the variable phi, and that variable is not a function of p, even if p is not a constant within the whole problem we can regard it as a constant within the integral.

 

[salman213]

But if I were to have any integral say

Integral of (ydx)

I have understand from my courses I cannot do this integral since y is not a function of x. But you are saying just treat it like a constant?

 

[The Dagda]

Pi and phi are constants yes.