language-icon Old Web
English
Sign In

Linearity of integration

In calculus, the integral of any linear combination of functions equals the same linear combination of the integrals of the functions; this property is known as linearity of integration. It is a fundamental property of the integral that encapsulates in a single rule two simpler rules of integration, the sum rule (the integral of the sum of two functions equals the sum of the integrals) and the constant factor rule (the integral of a constant multiple of a function equals a constant multiple of the integral). Linearity of integration is related to the linearity of summation, since integrals are thought of as infinite sums. In calculus, the integral of any linear combination of functions equals the same linear combination of the integrals of the functions; this property is known as linearity of integration. It is a fundamental property of the integral that encapsulates in a single rule two simpler rules of integration, the sum rule (the integral of the sum of two functions equals the sum of the integrals) and the constant factor rule (the integral of a constant multiple of a function equals a constant multiple of the integral). Linearity of integration is related to the linearity of summation, since integrals are thought of as infinite sums. Let f and g be functions. Now consider: By the sum rule in integration, this is By the constant factor rule in integration, this reduces to

[ "Applied mathematics", "Calculus", "Mathematical optimization", "Mathematical analysis" ]
Parent Topic
Child Topic
    No Parent Topic