? send me the full solution to solve this!!!!!!!!
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Originally Posted by kamaksh_ice ∫_0^∞▒((tan^(-1)〖ax-tan^(-1)〖bx)〗 〗)/ax dx Fix it!
reply me de full solution or else what? Originally Posted by kamaksh_ice ∫_0^∞▒((tan^(-1)〖ax-tan^(-1)〖bx)〗 〗)/ax dx what are these ? signs about? did you mean: ?
Amazingly this integral appears in my Advanced Calculus book so the credit is not mine (though I wish it was). First you must say . Confirm it is uniformly continous and do the following double integral trick. . Change order,
More generally If is continuous and the integral converges, This beautiful result is called Frullani's Integral. Nice, isn't it?
Last edited by Krizalid; Sep 24th 2007 at 06:27 PM.
Originally Posted by Krizalid More generally If is continuous and the integral converges, This beautiful result is called Frullani's Integral. Nice, isn't it? Yes it is nice . Where did you get that from? It seems MathWorld has it while Wikipedia does not. You should also state the conditions on the function* and limits. Perhaps . *)Maybe it should also be uniformly continous and having a limit at infinity?
I found (not mine) a proof of Frullani's Integral, and I'd like to share it Let So And Now let & The conclusion follows.
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