Indefinite integral and Fundalmental of calculus?

[pivoxa15]

Homework Statement

What is the connection between the Indefinite integral and the Fundalmental theorem of calculus (1st part)?

The Attempt at a Solution

They are the same to me but the FT is more formal.

 

[HallsofIvy]

You don't think there is any difference between an "integral" and a "theorem"? It makes no sense at all to say "they are the same". That's like saying a solution to a quadratic equation and the quadratic formula are "the same"! You have all the information you need. Now you need to think!

 

[pivoxa15]

Had a think. It seems to me that the indefinite integral is merely a notational convinience and not linked to anything else. The first part of the FT is the real deal (because integrals must be evaluated over an interval) and to simply the ideas, we introduce the indefinite integral to compute antiderivatives.

 

[HallsofIvy]

The fundamental theorem of calculus essentially says that you can find the definite integral (defined in terms of Riemann sums) by evaluating the indefinite integral at the limits of integration and subtracting.

 

[pivoxa15]

There are two parts to the FT. You were only referring to the second part?