Math Is Fun Forum

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

∫f(x)g(x)dx

I found this formula online and wondered if anyone can tell me if it is true.
There was no explanation with it.

Last edited by John E. Franklin (2005-12-27 13:43:53)

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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,339

Re: ∫f(x)g(x)dx

I have seen
∫udv=uv - ∫vdu.
This is exactly the same using f(x) and g(x) instead of u and v, hence its true.

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: ∫f(x)g(x)dx

Thank you.  So it is Integration by parts, I guess, just expressed with dv as g(x).   And u as f(x).   By the way, how come when you take the derivative of something, the dx usually isn't written down, but when you go backwards for the integral, you always write down the dx.  Shouldn't it be used in the answer of the derivative too?

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: ∫f(x)g(x)dx

Can this part be simplified any?  Is there a product rule for integration, or only derivatives?

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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: ∫f(x)g(x)dx

I believe you cant simplify anymore.