I need a hint for this problem -Definite Integrals-

[michonamona]

Homework Statement

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

Homework Equations

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

 

[Dick]

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

 

[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?

 

[Dick]

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

 

[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.

I appreciate your help.

M