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How do you find the derivative of this integral?

  1. Jan 16, 2005 #1
    [tex]\int_{0}^{x} [t \int_{1}^{t} f(u)du] dt[/tex]

    I don't know what to do. Thanks in advance
     
    Last edited: Jan 16, 2005
  2. jcsd
  3. Jan 16, 2005 #2

    dextercioby

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    1.1-st is to write the formula properly.

    Did u mean

    [tex] \frac{d}{dx}\{\int_{0}^{x} t[\int_{1}^{t} f(u)du] dt\} [/tex]

    ??

    Daniel.
     
  4. Jan 16, 2005 #3
    Yeah, that's it, but with no d/dx in the beginning. Sorry, I'm new to this latex stuff.

    [tex] \int_{0}^{x} [t \int_{1}^{t} f(u)du] dt [/tex]
     
  5. Jan 16, 2005 #4

    dextercioby

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    Okay,how about applying some Fundamental Theorem of calculus??

    Daniel.

    PS.Post your work.
     
  6. Jan 17, 2005 #5

    HallsofIvy

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    Your TITLE is "How do you find the derivative of this integral". That was why dextercioby put in the "d/dx".

    Fundamental theorem of calculus! [tex]\frac{d}{dx}\int_a^xF(t)dt= F(x)[/tex].

    Here, F(t) is [tex]t \int_{1}^{t} f(u)du] dt [/tex] so the derivative is
    [tex]x\int_1^xf(u)du[/tex]
     
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