Question

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

Answer 1

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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I hope that this was helpful.