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Constants and limits

pleasehelpme

New member
Feb 13, 2014
15
So I have this question: 2j2j5v6.jpg

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

Administrator
Staff member
Jan 26, 2012
4,040
Re: Constants and limits question?

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

Prove It

Well-known member
MHB Math Helper
Jan 26, 2012
1,403
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!
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.
 

pleasehelpme

New member
Feb 13, 2014
15
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

Administrator
Staff member
Jan 26, 2012
4,040
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.
 

pleasehelpme

New member
Feb 13, 2014
15
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

Well-known member
MHB Math Helper
Jan 26, 2012
1,403
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.