Constants & Limits: Integration & Anti-Derivative Q

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Discussion Overview

The discussion revolves around the concepts of integration and anti-derivatives in calculus, specifically focusing on the interpretation of formulas related to these topics. Participants explore the definitions and terminology associated with integration limits and the constant of integration.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether the first formula represents the theorem of integration and whether the second formula is an anti-derivative formula or another form of the integration formula.
  • Another participant suggests that the constant in the anti-derivative formula is typically referred to as the "constant of integration," rather than an "anti-derivative constant."
  • There is uncertainty expressed about whether the formula f(x)dx=F(x)+C is an anti-derivative formula or an integration formula, with participants reflecting on their understanding of these terms.
  • One participant notes that antidifferentiation is sometimes referred to as "indefinite integration," implying a connection between the two concepts.

Areas of Agreement / Disagreement

Participants express differing views on the terminology and classification of the formulas discussed, indicating that there is no consensus on whether f(x)dx=F(x)+C is strictly an anti-derivative formula or an integration formula.

Contextual Notes

Participants rely on specific definitions and interpretations that may vary, leading to ambiguity in the classification of the formulas. The discussion does not resolve these ambiguities.

pleasehelpme2
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So I have this question: View attachment 1970

And I just want to check my answer. Am I right? I think that the first formula is the theorem of integration so a and b are limits o integration and I'm not sure about the second formula, I think it's the anti derivative formula making that the anti derivative constant? Or is it another from of the integration formula, making it a constant of integration? Can you help? Thanks!
 

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Re: Constants and limits question?

Hmm, this seems a little pedantic for my taste but this article might help you out.
 
pleasehelpme said:
So I have this question: https://www.physicsforums.com/attachments/1970

And I just want to check my answer. Am I right? I think that the first formula is the theorem of integration so a and b are limits o integration and I'm not sure about the second formula, I think it's the anti derivative formula making that the anti derivative constant? Or is it another from of the integration formula, making it a constant of integration? Can you help? Thanks!

I would call C the constant of integration. There's no real reason it's not called an antiderivative constant, it's just I've never heard it be called that before.
 
Thanks...I'm just still not sure. Isn't f(x)dx=F(x)+C an antiderivative formula? or is it an integration formula? I honestly just can't remember. You're probably right but if it's an antiderivative formula then it's an antiderivative constant. I know F(x) is any antiderivative of f when F'(x)=f(x) but does that mean that f(x)dx=F(x)+C is an antiderivative formula?
 
If you look at the link I posted for you, you'll see it's called the "constant of integration". I would definitely go with that.
 
Yeah, you're right. Hopefully my professor will review all of the questions before our real test next week too. Thanks for all your help!
 
pleasehelpme said:
Thanks...I'm just still not sure. Isn't f(x)dx=F(x)+C an antiderivative formula? or is it an integration formula? I honestly just can't remember. You're probably right but if it's an antiderivative formula then it's an antiderivative constant. I know F(x) is any antiderivative of f when F'(x)=f(x) but does that mean that f(x)dx=F(x)+C is an antiderivative formula?

Antidifferentiation is sometimes called "indefinite integration", so it falls under integration.
 

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