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## Main Question or Discussion Point

under what condition the does the equality hold ?

[tex] \int_{0}^{\infty} dt \frac{ f(at)-f(bt)}{g(t)}= (G(b)-G(a))(f(0)-f(\infty)) [/tex]

and [tex] \int dt g(t) [/tex]

[tex] \int_{0}^{\infty} dt \frac{ f(at)-f(bt)}{g(t)}= (G(b)-G(a))(f(0)-f(\infty)) [/tex]

and [tex] \int dt g(t) [/tex]