Indefinite integral and Fundalmental of calculus?

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Homework Help Overview

The discussion revolves around the relationship between indefinite integrals and the Fundamental Theorem of Calculus, specifically its first part. Participants are exploring the conceptual connections and distinctions between these mathematical concepts.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants question the original poster's assertion that indefinite integrals and the theorem are the same, suggesting a need for deeper understanding. Others propose that the indefinite integral serves as a notational convenience linked to the broader implications of the theorem.

Discussion Status

The discussion is active, with participants offering differing perspectives on the nature of the indefinite integral and its relationship to the Fundamental Theorem of Calculus. There is an ongoing exploration of the definitions and implications of these concepts, with no clear consensus reached yet.

Contextual Notes

Participants are navigating potential misunderstandings about the terminology and the roles of integrals and theorems in calculus. The original poster's interpretation is being critically examined, highlighting the complexity of the topic.

pivoxa15
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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.
 
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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!
 
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.
 
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.
 
There are two parts to the FT. You were only referring to the second part?
 

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