Fundamental THeoreom of Cal

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?

Answers and Replies

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dextercioby
Science Advisor
Homework Helper
Yes...Use the Fundamental Theorem of Calculus...?? :uhh:

Daniel.

you need to find the antiderivative of that function, and then do F(3) - F(x) (correct me if im wrong anyone). But yeah, i believe thats what you have to do.

dextercioby
Science Advisor
Homework Helper
He cannot find the antiderivative among elementary functions...Yet he can solve the exercise without knowing it.

Daniel.

yeah well, im 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.

learningphysics
Homework Helper
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.

Hurkyl
Staff Emeritus
Science Advisor
Gold Member
People seem to forget that the fundamental theorem of calculus has two parts...

Hurkyl
Staff Emeritus
Science Advisor
Gold Member
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.

Hurkyl said:
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
Staff Emeritus
Science Advisor
Gold Member
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.