Integral Equality: \int f(x)g(x) = \int f(x) * \int g(x)

Vadim · 2005-05-13T17:37:26+00:00

just want to know if \int f(x)g(x)=\int f(x) * \int g(x)

Thread starter Vadim
Start date May 13, 2005
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Integral

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Homework Help Overview

The discussion revolves around the equality of integrals involving the product of two functions, specifically questioning whether \(\int f(x)g(x) = \int f(x) * \int g(x)\) holds true.

Discussion Character

Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

Participants explore the validity of the integral equality, with one participant confirming its falsehood and another seeking reassurance about their understanding. A reference to the derivative of a product is made to explain the reasoning behind the incorrectness of the equality.

Discussion Status

The discussion is active, with participants engaging in clarifying the misconception regarding the integral equality. Some guidance has been provided regarding the relationship between derivatives and integrals, particularly in the context of products of functions.

Contextual Notes

There is an underlying assumption that participants are familiar with basic integral and derivative concepts, as well as integration techniques such as integration by parts.

May 13, 2005

Vadim

just want to know if [tex]\int f(x)g(x)=\int f(x) * \int g(x)[/tex]

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May 13, 2005

arildno

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No, it is untrue.

May 13, 2005

Vadim

damn, that's what i thought, i just wanted to double check.

May 13, 2005

HallsofIvy

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Because (f(x)g(x))' is not f'(x)g'(x). It is (f(x)g(x))'= f'(x)g(x)+ f(x)g'(x). The "reverse" of that is "integration by parts" which can sometimes be used to integrate a product.