FTC and Integral

1. Jul 21, 2008

Sheneron

1. The problem statement, all variables and given/known data
$$F(x)= \int_1^x f(t)dt$$

$$f(t)= \int_1^{t^2} \frac{\sqrt{1+u^4}}{u} du$$

Find F''(2)

2. Relevant equations
Just learned the FTC part 1 and 2.

3. The attempt at a solution
Pretty lost on how to do this...

2. Jul 21, 2008

Defennder

You can write f(x) in terms of x: $$f(x) = \int^{x^2}_1 \frac{\sqrt{1+u^4}}{u} \ du$$. Now what can you say, by the FTC, about how F'(x) is related to f(x)? And how is this related to what you can do with the expression for f(x) given above?

3. Jul 21, 2008

Sheneron

F'(x) = f(x) for all x in (1,x^2) ?

And for the other part I am not sure... f(x) would equal F(x^2) - F(1) where F is the the anti derivative.

4. Jul 21, 2008

Defennder

You have F'(x) = f(x). You can see that F''(x) is f'(x), right? How would you get the latter from what you are given?

5. Jul 21, 2008

Sheneron

Take the derivative of f(x).

6. Jul 21, 2008

Sheneron

Alright I think understand. I will look over it some more. Thanks for your help.