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What is the constant of integration and why is it so important?

Answer 1

Christopher Agresta

If #F(x)# is an antiderivative of a function #f(x)#, that is,

#F'(x)=f(x)#,

then

#G(x)=F(x)+C#, where #C# is any constant,

is also an antiderivative of #f(x)# since

#G'(x)=[F(x)+C]'=F'(x)=f(x)#.

Hence, there are a family of functions (only differ by a constant) that are antiderivatives of #f(x)#. In order to include all antiderivatives of #f(x)#, the constant of integration #C# is used for indefinite integrals.

#int f(x)dx=F(x)+C#

The importance of #C# is that it allows us to express the general form of antiderivatives.

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