What does constant of integration mean?
Definitions for constant of integration
con·stant of in·te·gra·tion
This dictionary definitions page includes all the possible meanings, example usage and translations of the word constant of integration.
Wiktionary
constant of integrationnoun
An unspecified constant term added to a particular antiderivative to make it represent its whole family of antiderivatives, usually denoted with C.
Wikipedia
Constant of integration
In calculus, the constant of integration, often denoted by C {\displaystyle C} (or c {\displaystyle c} ), is a constant term added to an antiderivative of a function f ( x ) {\displaystyle f(x)} to indicate that the indefinite integral of f ( x ) {\displaystyle f(x)} (i.e., the set of all antiderivatives of f ( x ) {\displaystyle f(x)} ), on a connected domain, is only defined up to an additive constant. This constant expresses an ambiguity inherent in the construction of antiderivatives. More specifically, if a function f ( x ) {\displaystyle f(x)} is defined on an interval, and F ( x ) {\displaystyle F(x)} is an antiderivative of f ( x ) {\displaystyle f(x)} , then the set of all antiderivatives of f ( x ) {\displaystyle f(x)} is given by the functions F ( x ) + C {\displaystyle F(x)+C} , where C {\displaystyle C} is an arbitrary constant (meaning that any value of C {\displaystyle C} would make F ( x ) + C {\displaystyle F(x)+C} a valid antiderivative). For that reason, the indefinite integral is often written as ∫ f ( x ) d x = F ( x ) + C {\textstyle \int f(x)\,dx=F(x)+C} , although the constant of integration might be sometimes omitted in lists of integrals for simplicity.
Numerology
Chaldean Numerology
The numerical value of constant of integration in Chaldean Numerology is: 4
Pythagorean Numerology
The numerical value of constant of integration in Pythagorean Numerology is: 7
Translations for constant of integration
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- एकीकरण के निरंतरHindi
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"constant of integration." Definitions.net. STANDS4 LLC, 2024. Web. 29 Apr. 2024. <https://www.definitions.net/definition/constant+of+integration>.
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