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Homework Help: I need a hint for this problem -Definite Integrals-

  1. Mar 10, 2010 #1
    1. The problem statement, all variables and given/known data


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

    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. jcsd
  3. Mar 10, 2010 #2

    Dick

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    Your derivatives are with respect to x, right? Look up the Leibniz integral rule.
     
  4. Mar 11, 2010 #3
    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?
     
  5. Mar 11, 2010 #4

    Dick

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    Ok, factor x out. It's not a function of t. Now use the product rule and the fundamental theorem of calculus.
     
  6. Mar 11, 2010 #5
    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
     
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