MHB Constants & Limits: Integration & Anti-Derivative Q

[pleasehelpme2]

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!

 

[Jameson]

Re: Constants and limits question?

Hmm, this seems a little pedantic for my taste but this article might help you out.

 

[Prove It]

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.

 

[pleasehelpme2]

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?

 

[Jameson]

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.

 

[pleasehelpme2]

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!

 

[Prove It]

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.