# Fundamental theorem of calculus

1. Mar 2, 2006

### jesuslovesu

(that's a 3 on the last integral)
http://img131.imageshack.us/img131/2549/jesus1cj.png [Broken]

I need to find which of those are true, now I thought I and III were true
for sure. But when I do II with an example f(x) = x^2 I get x^2 - 9, so it's not true right? (I and III are not choices given for the correct answer)

I know the fundamental theorem of calculus states that the derivative
of an integral is just the function.

Last edited by a moderator: May 2, 2017
2. Mar 2, 2006

### 0rthodontist

Yes, II is not true in general. Why not make a test function for the others also?

You might want to look again at the precise statement of the fundamental theorem of calculus.

3. Mar 2, 2006

### topsquark

Consider what kind of integral we are talking about in I. Consider:
$$\int_0^3x^2 \, dx = (1/3)x^3|_0^3=9 \neq x^2$$.

-Dan

Last edited by a moderator: May 2, 2017
4. Mar 4, 2006

### VietDao29

One thing to remember is that:
$$\mathop {\int} \limits_{0} ^ 3 f(x) dx$$ is some specific number, whose derivative with respect to x is just a plain 0.
While this:
$$\mathop {\int} \limits_{0} ^ x f(x) dx$$ is different, since the result does depend on what x you choose. And it's a function of x.
Can you get this? :)

Last edited: Mar 4, 2006
5. Mar 4, 2006

### HallsofIvy

Staff Emeritus
Okay, you see that if you try some simple function in 2, you get different results on left and right (differ by a constant) so that is not correct.

It has been pointed out that 1 is obviously untrue (the derivative of a constant is 0).

What about 3? Choose some simple functions and see what happens. Of course, examples won't prove a general statement is true but think about the "Fundamental Theorem of Calculus".