Integral Equality: \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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The equation ∫ f(x)g(x) = ∫ f(x) * ∫ g(x) is incorrect. The derivative of the product f(x)g(x) is not equal to the product of their derivatives, as shown by the product rule. Instead, the correct derivative is (f(x)g(x))' = f'(x)g(x) + f(x)g'(x). Integration by parts is a method that can be applied to integrate products of functions. Understanding these principles is crucial for accurate integration techniques.

May 13, 2005

Vadim

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

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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.

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