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Constant of integration

Constant Con"stant, n. 1. (Astron.) A number whose value, when ascertained (as by observation) and substituted in a general mathematical formula expressing an astronomical law, completely determines that law and enables predictions to be made of its effect in particular cases. 2. (Physics) A number expressing some property or condition of a substance or of an instrument of precision; as, the dielectric constant of quartz; the collimation constant of a transit instrument. Aberration constant, or Constant of aberration (Astron.), a number which by substitution in the general formula for aberration enables a prediction to be made of the effect of aberration on a star anywhere situated. Its value is 20[sec].47. Constant of integration (Math.), an undetermined constant added to every result of integration. Gravitation constant (Physics), the acceleration per unit of time produced by the attraction of a unit of mass at unit distance. When this is known the acceleration produced at any distance can be calculated. Solar constant (Astron.), the quantity of heat received by the earth from the sun in a unit of time. It is, on the C. G. S. system, 0.0417 small calories per square centimeter per second. --Young.

Constant Con"stant, n. 1. (Astron.) A number whose value, when ascertained (as by observation) and substituted in a general mathematical formula expressing an astronomical law, completely determines that law and enables predictions to be made of its effect in particular cases. 2. (Physics) A number expressing some property or condition of a substance or of an instrument of precision; as, the dielectric constant of quartz; the collimation constant of a transit instrument. Aberration constant, or Constant of aberration (Astron.), a number which by substitution in the general formula for aberration enables a prediction to be made of the effect of aberration on a star anywhere situated. Its value is 20[sec].47. Constant of integration (Math.), an undetermined constant added to every result of integration. Gravitation constant (Physics), the acceleration per unit of time produced by the attraction of a unit of mass at unit distance. When this is known the acceleration produced at any distance can be calculated. Solar constant (Astron.), the quantity of heat received by the earth from the sun in a unit of time. It is, on the C. G. S. system, 0.0417 small calories per square centimeter per second. --Young.

- 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...

- regardless of its value. Therefore the antiderivative is only determined up to an unknown constant term, which is called "the constant of integration" and added...

- variable of integration. During the evaluation of a limit, a constant remains the same as it was before and after evaluation. Integration of a function of one...

- (a special case of integration by substitution) Integration by parts (to integrate products of functions) Inverse function integration (a formula that...

- integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of...

- {\displaystyle C} is an arbitrary constant of integration. This procedure is frequently used, but not all integrals are of a form that permits its use. In...

- dx=\sin x+C} where C, the constant of integration, is an arbitrary fixed real number. In other words, whatever the value of C, differentiating sin x +...

- The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus, and...

- and integrate: y ′ y = f , log y = k + F , {\displaystyle {\frac {y'}{y}}=f,\qquad \log y=k+F,} where k is an arbitrary constant of integration and...

- − λ t + C {\displaystyle \ln N=-\lambda t+C\,} where C is the constant of integration, and hence N ( t ) = e C e − λ t = N 0 e − λ t {\displaystyle...

- regardless of its value. Therefore the antiderivative is only determined up to an unknown constant term, which is called "the constant of integration" and added...

- variable of integration. During the evaluation of a limit, a constant remains the same as it was before and after evaluation. Integration of a function of one...

- (a special case of integration by substitution) Integration by parts (to integrate products of functions) Inverse function integration (a formula that...

- integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of...

- {\displaystyle C} is an arbitrary constant of integration. This procedure is frequently used, but not all integrals are of a form that permits its use. In...

- dx=\sin x+C} where C, the constant of integration, is an arbitrary fixed real number. In other words, whatever the value of C, differentiating sin x +...

- The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus, and...

- and integrate: y ′ y = f , log y = k + F , {\displaystyle {\frac {y'}{y}}=f,\qquad \log y=k+F,} where k is an arbitrary constant of integration and...

- − λ t + C {\displaystyle \ln N=-\lambda t+C\,} where C is the constant of integration, and hence N ( t ) = e C e − λ t = N 0 e − λ t {\displaystyle...

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