I need a hint for this problem -Definite Integrals-

  • #1
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Homework Statement




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]

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
 

Answers and Replies

  • #2
Dick
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Your derivatives are with respect to x, right? Look up the Leibniz integral rule.
 
  • #3
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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
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.
 
  • #5
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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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