Results 1 to 2 of 2

Math Help - Centroid question

  1. #1
    Junior Member
    Nov 2009

    Centroid question

    Find the x-coordinate of the centroid of the region bounded by the following curves: y=x^2,y=x+6.
    Hint: Make a sketch and use symmetry where possible.
    x-coordinate of Centroid:

    I got the wrong answer but I came up with 558/740.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Dec 2008
    I came up with a different answer, but we may start by finding the value of x for which y=x^2 and y=x+6 intersect:

    \begin{aligned}<br />
x^2&=x+6\\<br />
x^2-x-6&=0\\<br />
(x-3)(x+2)&=0.<br />

    Our limits of integration are therefore x=-2,3. giving us the area of the region:

    A=\int_{-2}^3 (x+6)-x^2\,dx.

    To find the x-coordinate of the centroid, we just calculate

    \bar{x}=\frac{1}{A}\int_{-2}^3 x((x+6)-x^2)\,dx.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Centroid...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 28th 2010, 12:58 PM
  2. Replies: 2
    Last Post: November 7th 2009, 08:56 PM
  3. Replies: 1
    Last Post: April 21st 2009, 12:06 AM
  4. Centroid
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: April 10th 2009, 11:06 AM
  5. Centroid
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 3rd 2008, 01:56 PM

Search Tags

/mathhelpforum @mathhelpforum