Function manipulation involving trigonometry

[shanepitts]

I'm trying to integrate a function in a classical physics problem but when I apply the limits it gave undefined results. Hence, I looked up that particular part of the solution and I did not fathom the function manipulation. It states that if x≤b in the following expression:

∫{[x/b]/[1-(x/b)]}^1/2 d(x/b)

then x/b=sin²θ

is this statement true?

If so, how can this be?

Thanks in advance

 

[haruspex]

I think it is saying that if x≤b then it is valid to make that variable change. But in fact you need 0≤x/b≤1.

 

[Noctisdark]

Hi shanepitts ,
You make make any substitution you like but, people often go through changing variable in order to make things simple, if you pose x/b = sin^2, things will become horribly complicated (at least for me) so what i suggest is making a simpler substitution, what do you think of u =sqrt(x/b) ;) ?

 

[haruspex]

if you pose x/b = sin^2, things will become horribly complicated (at least for me)

Not for me. Comes out quite simply. But this wasn't the point of the OP anyway, I think.