# Thread: Fundamental Theorem of Calculus

1. ## Fundamental Theorem of Calculus

Working on some homework problems, and kind of stuck. I thought I had a handle on this, but not so much.

Here is the problem:

What I did is take the anti derivative, which is t^5/5.. then plug in the values and subtract. So I get 20^5/5 - x^5/5 to be the answer.. but thats wrong. I don't know if I'm missing a step or doing something wrong. Any help would be greatly appreciated.

Thanks!

2. Originally Posted by Chetti
Working on some homework problems, and kind of stuck. I thought I had a handle on this, but not so much.

Here is the problem:

What I did is take the anti derivative, which is t^5/5.. then plug in the values and subtract. So I get 20^5/5 - x^5/5 to be the answer.. but thats wrong. I don't know if I'm missing a step or doing something wrong. Any help would be greatly appreciated.

Thanks!
I'm sorry, but I don't see the integral... xD

3. Is it $\int_{x}^{20} t^4 \ dt$?

4. yes, its t^4 (thats the integral) and the limits are 20 (a) and x (b)

5. Originally Posted by Chetti
yes, its t^4 (thats the integral) and the limits are 20 (a) and x (b)
Then it would be $\frac{x^5}{5}- \frac{20^{5}}{5}$.

6. Thanks! I can't log into where I have to go to try that, but its a little different from what I was trying to do.

Thanks again!!

7. The answer was wrong. I eventually did get the right answer, and I will post back with it, I need to log in to the site and get it. BUT, I was missing a step.

Here are the steps: antiderivative, then plug in the limits then take the derivative, then subtract.. then you get the answer. I was so confused. I'm still confused.

8. $\int_x^{20} t^4 \, dt = \frac{20^5}{5} - \frac{x^5}{5}$

but why do I get the feeling that this is not all there is to it?

note that the original "problem" was given as a function ... $f(x) = \int_x^{20} t^4 \, dt$

sure you weren't supposed to find $f'(x)$ ?

9. If you are looking for $f'(x)$ ...

$f(x)=\int_{x}^{20}t^{4}\; dt = - \int_{20}^{x}t^4\; dt \; ,\Rightarrow f'(x)= -x^{4}$