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Math Help - Differentiating integral functions

  1. #1
    Senior Member I-Think's Avatar
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    Differentiating integral functions

    Need to make sure I'm getting this right

    Is

    A) \frac{d}{dx}\int_3^{e{^x^2}} ln(t^3) dt=2x^3e^x^2<br />
    and

    B) \frac{d}{dx}\int_a^x \frac{f(t}{t^2}=\frac{-2f(x)}{x}
    Last edited by I-Think; February 8th 2011 at 10:07 PM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by I-Think View Post
    A) \frac{d}{dx}\int_3^e^x^2 ln(t^3) dt=2x^3e^x^2<br />

    It is not clear what the integrand function and limits are.


    B) \frac{d}{dx}\int_a^x \frac{f(t}{t^2}=\frac{-2f(x)}{x}

    \dfrac{d}{dx}\displaystyle\int_a^x \dfrac{f(t)}{t^2}dt=\dfrac{f(x)}{x^2}





    Fernando Revilla
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  3. #3
    Senior Member I-Think's Avatar
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    For A), integrating ln(t^3) between e^x^2 and 3
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Using the Fundamental Theorem of Calculus an the Chain's Rule:

    \dfrac{d}{dx}\displaystyle\int_a^{g(x)} f(t)dt=f[g(x)]g'(x)

    Let us see what do you obtain.


    Fernando Revilla
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