Results 1 to 4 of 4

Math Help - Find the minimum of the integral

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    10

    Find the minimum of the integral

    Hi all, I got set this question as part of my calculus of variations homework, but the lecturer has told me that it's not actually a calculus of variations problem (just a calculus problem).

    Find the minimum of the integral:

    I = \int{(2(y+2)^3\frac{dy}{dx}}+(x-7))dx

    I'm not sure whether I should do something involving Leibniz's rule, or whether I should try integrating, then differentiating twice.

    So far I got:

    I = {\frac{1}{2}(y+2)^4+\frac{1}{2}x^2-7x,

    since

    \frac{d}{dx}(\frac{1}{2}(y+2)^4) = 2(y+2)^3\frac{dy}{dx}

    Any hints?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Set dI/dx = 0. What do you get?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2010
    Posts
    10
    2(y+2)^3\frac{dy}{dx}}+(x-7) = 0

    Take the (x-7) to the other side and integrate both sides, gives the same as in my first post; I = {\frac{1}{2}(y+2)^4+\frac{1}{2}x^2-7x, which confuses me, does dI/dx = I here?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Correct. For finding out about min or max, try taking the second derivative and see what you get. If you can show that the second derivative is positive for the solution of the first-order DE above that you need to solve, then you've got a min. In CoV problems, I'm afraid they often don't do the second-order checking necessary to discover if you're dealing with a max or a min.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Find the minimum of an integral
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: December 19th 2011, 10:30 AM
  2. Find a minimum value
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 29th 2009, 05:53 AM
  3. Find the minimum value
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 16th 2008, 03:55 AM
  4. find the minimum
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 6th 2007, 07:20 PM
  5. Find minimum value
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 11th 2006, 02:19 PM

Search Tags


/mathhelpforum @mathhelpforum