Constants & Limits: Integration & Anti-Derivative Q

In summary: The formula f(x)dx=F(x)+C is called the indefinite integral formula or the antiderivative formula. In summary, the first formula mentioned is the theorem of integration with a and b as limits of integration. The second formula, f(x)dx=F(x)+C, is an antiderivative formula or indefinite integral formula used in integration. C is referred to as the constant of integration.
  • #1
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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  • #2
Re: Constants and limits question?

Hmm, this seems a little pedantic for my taste but this article might help you out.
 
  • #3
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.
 
  • #4
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?
 
  • #5
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.
 
  • #6
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!
 
  • #7
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.
 

FAQ: Constants & Limits: Integration & Anti-Derivative Q

What is the definition of a constant in integration?

A constant in integration is a number that is added to the indefinite integral of a function. It is represented by the letter "C" and is used to account for all possible solutions to the integral equation.

How do you know when to use integration to find the area under a curve?

You can use integration to find the area under a curve when you have a function that represents the curve and the limits of the area you want to find. The integral of the function between the given limits will give you the area under the curve.

What is the difference between definite and indefinite integration?

Definite integration involves finding the value of the integral between two given limits, while indefinite integration involves finding the general antiderivative of a function without specifying any limits.

How do you use integration to solve real-world problems?

Integration can be used to solve real-world problems by representing the problem as a mathematical function, finding the appropriate limits, and then integrating the function to find the solution. This can be applied to problems in physics, economics, and other fields.

Can all functions be integrated?

No, not all functions can be integrated. Some functions, such as trigonometric functions and exponential functions, have specific rules for integration. However, there are some functions that do not have an antiderivative and therefore cannot be integrated using traditional methods.

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