1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: I need a hint for this problem -Definite Integrals-
Loading...