# Fundamental THeoreom of Cal

1. Jan 25, 2005

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

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

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

2. Jan 25, 2005

### dextercioby

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

Daniel.

3. Jan 25, 2005

### ziddy83

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.

4. Jan 25, 2005

### dextercioby

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

Daniel.

5. Jan 25, 2005

### ziddy83

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

6. Jan 25, 2005

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

7. Jan 25, 2005

### learningphysics

8. Jan 25, 2005

### Hurkyl

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

9. Jan 25, 2005

### Hurkyl

Staff Emeritus
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.

10. Jan 26, 2005

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