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Topic: Why do we use capital F for antiderivative?
Replies: 2   Last Post: Oct 25, 2013 11:11 AM

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 neuronet Posts: 24 Registered: 10/18/12
Why do we use capital F for antiderivative?
Posted: Oct 25, 2013 10:14 AM

Why do we use capital F for the antiderivative of f, instead of simply f?

Consider the general equation df/dt=g [1]

Note I assume f and g are scalar functions of t.

To find the function f whose derivative is g, we simply take the antiderivative of g. So (using int(X) for indefinite integral of X) we can integrate both sides of [1]:

int(df/dt)=int(g)=f+C [2]

Note the integral of df/dt is simply f(t) (with a constant added). So why is it conventional to use capital letter F for int(g), instead of just calling it f? That is, why add a '=F' to the end of [2]?

Why is this universal in the textbooks? What am I missing, as right now it looks like an unnecessary terminological layer, that even seems to hide the elegance of the relationship between the derivative and antiderivative?