Constants & Limits: Integration & Anti-Derivative Q

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SUMMARY

The discussion centers on the concepts of integration and anti-derivatives in calculus. The first formula mentioned, f(x)dx=F(x)+C, is confirmed as the anti-derivative formula, where C represents the constant of integration. Participants clarify that while the term "antiderivative constant" is not commonly used, it is synonymous with the constant of integration. The conversation emphasizes the relationship between limits of integration and the process of antidifferentiation, reinforcing the foundational principles of calculus.

PREREQUISITES
  • Understanding of basic calculus concepts, including integration and differentiation.
  • Familiarity with the notation of integrals and anti-derivatives.
  • Knowledge of the Fundamental Theorem of Calculus.
  • Ability to interpret mathematical formulas and their components.
NEXT STEPS
  • Study the Fundamental Theorem of Calculus in detail.
  • Learn about the properties of definite and indefinite integrals.
  • Explore examples of integration techniques, including substitution and integration by parts.
  • Review common mistakes in interpreting integration and anti-derivative concepts.
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Students of calculus, mathematics educators, and anyone preparing for calculus examinations will benefit from this discussion, particularly those seeking clarity on integration and anti-derivative concepts.

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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