Results 1 to 3 of 3

Math Help - Sum of squares from 0 to 1

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    4

    Sum of squares from 0 to 1

    The integral from 0 to 1 of x^2 is equivalent to the integral from 0 to 1 of the sum of the first n squares formula (x(2x+1)(x+1)/6) does anyone know if this is some special occurrence (it's only true for 0 to 1 as far as I can tell).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    Hmm..



    I guess this is only a coincidence.

    \int \frac{ x (x+1) (2x+1)}{6} ~dx = \frac{x^2}{12}+\frac{x^3}{6}+\frac{x^4}{12}

    \int x^2 ~dx = \frac{x^3}{3}


    \frac{1^2}{12}+\frac{1^3}{6}+\frac{1^4}{12}=\frac{  1^3}{3} = \frac{1}{3}

    \frac{0^2}{12}+\frac{0^3}{6}+\frac{0^4}{12}=\frac{  0^3}{3} = 0

    I don't know, such things are likely to happen with numbers 0 and 1.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Coincidence at best.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sum of squares
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: October 16th 2010, 07:25 PM
  2. Magic squares of Squares
    Posted in the Math Puzzles Forum
    Replies: 5
    Last Post: September 22nd 2010, 10:58 AM
  3. Squares
    Posted in the Math Puzzles Forum
    Replies: 6
    Last Post: December 2nd 2009, 07:55 PM
  4. Replies: 4
    Last Post: November 13th 2009, 06:12 PM
  5. sum of squares
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 7th 2007, 08:19 AM

Search Tags


/mathhelpforum @mathhelpforum