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

[ProBasket]

Use part I of the Fundamental Theorem of Calculus to find the derivative of

\int_x^{3} sin(x^3) dx

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

i think i need to integrate the problem first, but it seems impossible. can someone help?

 

[dextercioby]

Yes...Use the Fundamental Theorem of Calculus...??

Daniel.

 

[ziddy83]

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.

 

[dextercioby]

He cannot find the antiderivative among elementary functions...Yet he can solve the exercise without knowing it.

Daniel.

 

[ziddy83]

yeah well, I am usually Being helped instead of Helping others...so...hey i tried

 

[ProBasket]

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.

 

[learningphysics]

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.

 

[Hurkyl]

People seem to forget that the fundamental theorem of calculus has two parts...

 

[Hurkyl]

By the way, please tell me that you copied the problem down incorrectly and it actually says:

\int_x^{3} \sin t^3 \, dt

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

 

[ProBasket]

By the way, please tell me that you copied the problem down incorrectly and it actually says:

\int_x^{3} \sin t^3 \, dt

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 \int_x^{3} \sin t^3 \, dt


sorry about the typo

 

[cepheid]

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.