Changing Limits of Integration affects variable substitution?

[DrMath]

1. The problem statement, all variables and given/known data

see attached

2. Relevant equations



3. The attempt at a solution

[lanedance]

not exactly sure what the question is...

couple of points though, it is usually easier to use a different dummy variable when you use a subtitution

say you have
\int_b^a dt f(t)

and want to change to u(t) = t/2, then
t=2u
dt = 2.du
u(a) = a/2
u(b) = b/2

so the integral becomes
\int_{b/2}^{a/2} 2.du f(2u)

see how this compares with your case...

[DrMath]

thanks