Definition of Antiderivative
A function \(F\) is an antiderivative of \(f\) on an interval \(I\) when \(F'(x) = f(x)\) for all \(x\) in \(I\).
A function \(F\) is an antiderivative of \(f\) on an interval \(I\) when \(F'(x) = f(x)\) for all \(x\) in \(I\).
Representation of Antiderivatives
If \(F\) is an antiderivative of \(f\) on an interval \(I\), then \(G\) is an antiderivative of \(f\) on the interval \(I\) if and only if \(G\) is of the form \(G(x) = F(x) +C\), for all \(x\) in \(I\) where \(C\) is a constant.
If \(F\) is an antiderivative of \(f\) on an interval \(I\), then \(G\) is an antiderivative of \(f\) on the interval \(I\) if and only if \(G\) is of the form \(G(x) = F(x) +C\), for all \(x\) in \(I\) where \(C\) is a constant.