Calculus - Center of Mass

Find the exact coordinates of the centroid given the curves: y = 1/x, y = 0, x = 1, x = 2.

X = 1/Area*Integral from a to b: x*f(x)dx
Y = 1/Area*Integral from a to b: [(1/2)*(f(x))^2]dx

How do I find the area for this? Once I know that, is this the correct set up?

X = 1/Area*Integral from 1 to 2: [x*(1/x)]dx
X = 1/Area*[x] evaluated at 1 and 2

Y = 1/Area*Integral from 1 to 2:
[(1/2)*(1/x)^2]dx
Y = 1/Area*[(-1/x] evaluated at 1 and 2.

Thanks.

area= INT y dx =INT dx/x= ln x from 1,2

yES, Those are the correct equations for the first moment.

Ok, thanks for checking and for helping.

  1. 👍 0
  2. 👎 0
  3. 👁 300
asked by COFFEE

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    could some body please check this for me? 1. find the exact coordinates of the centroid of the region bounded by y-x^2, the x axis, the y axis, and the line x=1? I said the answer was ((3/4), (3/10)) 2. Find the exact coordinates

    asked by tia on April 6, 2008
  2. calculus

    Find the specified coordinates of the centroid of the area bounded by a) x=3 and 2x=y^2 find the coordinates x and y of the centroid b) y= x^3 and y=4x in the first quadrant. Find the x coordinate of the centroid

    asked by harry on April 11, 2013
  3. geometry

    Triangle PQR has vertices P(1,2), Q(25,2) and R(10,20). Find the coordinates of the centroid. Find the coordinates of the circumcenter. Find the coordinates of the orthocenter. Find the equation of the line.

    asked by Ginny on April 24, 2011
  4. Calculus

    Find the exact coordinates of the centroid. y = sqrt[x], y = 0, x = 9. -------------- Is this basically 1/4 of an oval/ellipse? If so then the area would be: pi*9*3, correct? So the X coordinate would equal: 1/Area * Integral from

    asked by COFFEE on June 17, 2007
  5. calc

    Find the centroid of the region bounded by the given curves. y = 2 sin 3x, y = 2 cos 3x, x = 0, x = π/12

    asked by Zoey on July 8, 2014
  6. calculus

    find the centroid of the plane region bounded by the curves y = cos x, y=sinx, x=0,

    asked by zoe on October 31, 2011
  7. calculus 2

    Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. (Round your answer to two decimal places.) y = 8x^2− 3x, y

    asked by TayB on January 22, 2016
  8. Geometry

    How do you find the centroid of the coordinates D(-3, 8), E(-3, 0) and F(9, 4). What are the steps?

    asked by Camile on February 8, 2011
  9. math

    Find the coordinates of the centroid of the regions bounded by the graphs of: i)y=x2+1,x=0,x=1 and y=0 ii)y+x2=6 and y+2x-3=0

    asked by islam on May 3, 2010
  10. math

    find the coordinates of the centroid of a triangular metal part with vertices at A(12,18) B(18,6), and C(3,12)

    asked by Ted on October 25, 2010

More Similar Questions