What is the FTC saying about the derivative of the integral of a function?

  • Thread starter Thread starter ProBasket
  • Start date Start date
  • Tags Tags
    Fundamental
Click For Summary

Homework Help Overview

The discussion revolves around the application of the Fundamental Theorem of Calculus (FTC) in finding the derivative of a definite integral involving the function sin(x^3). Participants are exploring the relationship between integration and differentiation as outlined by the FTC.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to clarify the application of the FTC, with some suggesting the need to find an antiderivative and others questioning the notation used in the problem. There are discussions about whether the integral can be solved using elementary functions and the implications of the FTC's two parts.

Discussion Status

The discussion is active, with participants providing insights and questioning assumptions about the problem setup. Some guidance has been offered regarding the FTC, but there is no explicit consensus on the approach to take.

Contextual Notes

There is a noted confusion regarding the notation used in the integral, with participants pointing out potential misinterpretations. The original poster acknowledges a typo in the problem statement, which may affect the understanding of the question.

ProBasket
Messages
140
Reaction score
0
Use part I of the Fundamental Theorem of Calculus to find the derivative of

[tex]\int_x^{3} sin(x^3) dx[/tex]

F'(x)=_________________ (answer goes here)

i think i need to integrate the problem first, but it seems impossible. can someone help?
 
Physics news on Phys.org
Yes...Use the Fundamental Theorem of Calculus...?? :rolleyes:

Daniel.
 
you need to find the antiderivative of that function, and then do F(3) - F(x) (correct me if I am wrong anyone). But yeah, i believe that's what you have to do.
 
He cannot find the antiderivative among elementary functions...Yet he can solve the exercise without knowing it.

Daniel.
 
yeah well, I am usually Being helped instead of Helping others...so...hey i tried
 
dextercioby said:
He cannot find the antiderivative among elementary functions...Yet he can solve the exercise without knowing it.

Daniel.


isnt the "Fundamental Theorem of Calculus" just solving it as a regular integral? that's what i thought it was.
 
ProBasket said:
isnt the "Fundamental Theorem of Calculus" just solving it as a regular integral? that's what i thought it was.

Read your question carefully. What is the question asking you for? I believe that you've misread the question.
 
People seem to forget that the fundamental theorem of calculus has two parts...
 
By the way, please tell me that you copied the problem down incorrectly and it actually says:

[tex]\int_x^{3} \sin t^3 \, dt[/tex]

If not, then bear in mind that your source is using poor notation -- they used the symbol x to represent two very different things.
 
  • #10
Hurkyl said:
By the way, please tell me that you copied the problem down incorrectly and it actually says:

[tex]\int_x^{3} \sin t^3 \, dt[/tex]

If not, then bear in mind that your source is using poor notation -- they used the symbol x to represent two very different things.


sorry, i did copied it down wrong without knowing. your right, it's [tex]\int_x^{3} \sin t^3 \, dt[/tex]


sorry about the typo
 
  • #11
Okay...in simplistic terms, what is the FTC saying? I.e. "the derivative of the integral of the function is...?" Answer that, and you have this question. Just review the FTC.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
1K
Replies
5
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
Replies
28
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K