Results 1 to 2 of 2

Thread: Derivative of an Integral Question

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    14

    Derivative of an Integral Question

    Find $\displaystyle \frac {d^2}{dx^2} \int^x_0(\int^{sint}_1 \sqrt{1+u^4}du)dt$

    So these were my steps:

    $\displaystyle \frac {d}{dx} (\frac {d}{dx}\int^x_0(\int^{sint}_1 \sqrt{1+u^4}du)dt)$


    $\displaystyle \frac {d}{dx} (\int^{sint}_1 \sqrt{1+x^4}dt)$

    I am not sure if i followed the FTC correctly with the inside d/dx and integral by changing u to x, if I did I think I managed to follow the rest through correctly the prebious part was what I was confused on.

    $\displaystyle \sqrt{1+sint^4}(sint) dt$

    $\displaystyle \sqrt{1+sint^4}(cost)$

    I think I was suppose to start from the inside and go out but I did not know anyway to integrate $\displaystyle \sqrt{1+u^4}$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,656
    Thanks
    14
    Put $\displaystyle f(x)=\int_0^x g(t)\,dt,$ where $\displaystyle g(t)=\int_1^{\sin t}\sqrt{1+u^4}\,du,$ then $\displaystyle f'(x)=\int_1^{\sin x}\sqrt{1+u^4}\,du$ so $\displaystyle f''(x)$ ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative of a integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 21st 2011, 04:22 PM
  2. Derivative of a Integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 11th 2010, 04:12 PM
  3. Derivative of an integral
    Posted in the Calculus Forum
    Replies: 7
    Last Post: Feb 7th 2010, 12:30 AM
  4. Derivative of an integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Sep 9th 2009, 11:25 AM
  5. Derivative and Definite Integral question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Apr 9th 2006, 06:38 AM

Search Tags


/mathhelpforum @mathhelpforum