# Problem:Commutative property of definite integral

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• Aug 16th 2011, 05:33 AM
x3bnm
Problem:Commutative property of definite integral
Is it possible to prove the following

$\displaystyle \int_a^b f(x)\;g(x)\;dx = \int_a^b g(x)\;f(x)\;dx$

I know it's true but how do you prove this? Thanks.
• Aug 16th 2011, 05:57 AM
CaptainBlack
Re: Problem:Commutative property of definite integral
Quote:

Originally Posted by x3bnm
Is it possible to prove the following

$\displaystyle \int_a^b f(x)\;g(x)\;dx = \int_a^b g(x)\;f(x)\;dx$

I know it's true but how do you prove this? Thanks.

Is that really what you mean?

If f and g are real or complex valued functions it follows from commutativity of multiplication.

CB
• Aug 16th 2011, 06:20 AM
x3bnm
Re: Problem:Commutative property of definite integral
Quote:

Originally Posted by CaptainBlack
Is that really what you mean?

If f and g are real or complex valued functions it follows from commutativity of multiplication.

CB

Thanks CaptainBlack. That answers my question.