Results 1 to 5 of 5

Math Help - Derivative of an integral

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    13

    Derivative of an integral

    Hi, how do you solve this (btw, sorry, I don't know how to make snazzy math grafics :/):

    Find G'(x) for G(x) = the integral exp(t^2)dt in the interval 1/x< a< x.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by Hampus View Post
    Hi, how do you solve this (btw, sorry, I don't know how to make snazzy math grafics :/):

    Find G'(x) for G(x) = the integral exp(t^2)dt in the interval 1/x< a< x.
    \frac{d}{dx} \int_v^u f(t) \, dt = f(u) \cdot \frac{du}{dx} - f(v) \cdot \frac{dv}{dx}


    G(x) = \int_{\frac{1}{x}}^x e^{t^2} \, dt

    G'(x) = e^{x^2} + \frac{e^{\frac{1}{x^2}}}{x^2}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    13
    Could you maybe explain why this is the case? (please?)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    Quote Originally Posted by Hampus View Post
    Could you maybe explain why this is the case? (please?)
    Say that \int e^{t^2}\,dt=F(t). (It doesn't matter what F(t) is.)

    So \int_{1/x}^x e^{t^2}\,dt=F(x)-F(1/x) by the Fundamental Theorem of Calculus.

    To take the derivative of this expression, use the chain rule to get

    F'(x)\cdot1-F'(1/x)\cdot-\frac{1}{x^2}

    But because of how we defined F, we know that F'(x)=e^{x^2}.

    So the above is e^{x^2}+\frac{e^{1/x^2}}{x^2}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2009
    Posts
    13
    Feels like something I could have figured out if I gave it a thought :/ Thanks a lot though, very helpful, it all makes sense
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative of an integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 3rd 2010, 05:34 AM
  2. derivative of an integral?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 8th 2009, 04:56 PM
  3. derivative of an integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 19th 2009, 04:18 PM
  4. Derivative of an integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 9th 2009, 11:25 AM
  5. derivative of an integral
    Posted in the Calculus Forum
    Replies: 9
    Last Post: April 17th 2008, 08:21 AM

Search Tags


/mathhelpforum @mathhelpforum