# I need a hint for this problem -Definite Integrals-

1. Mar 10, 2010

### michonamona

1. The problem statement, all variables and given/known data

Let F(x) = $$\int^{x}_{0}xe^{t^{2}}dt$$ for $$x\in[0,1]$$. Find F''(x) for x in (0,1). Caution: $$F'(x)\neq xe^{x^{2}}$$

2. Relevant equations

3. The attempt at a solution
I just need a hint. I know what F"(x) is already (solution was given), but I'd like to find F'(x)

Thank you

M

2. Mar 10, 2010

### Dick

Your derivatives are with respect to x, right? Look up the Leibniz integral rule.

3. Mar 11, 2010

### michonamona

Thanks for your reply. This is from an Analysis course so we didn't cover Leibniz's integral rule. Can you offer any additional hints?

4. Mar 11, 2010

### Dick

Ok, factor x out. It's not a function of t. Now use the product rule and the fundamental theorem of calculus.

5. Mar 11, 2010

### michonamona

Thank you very much for your prompt reply. I never thought about factoring out the x. So I guess that was standard procedure. Any variables that is not a function of t may be factored out.