calculus

posted by .

find the centroid of the region bounded by x^2-12x and the x-axis

  • calculus -

    The expression x²-12x crosses the x-axis twice, at x=0 and x=12.

    The curve stays below the x-axis on the interval [0,12].

    See:
    http://img207.imageshack.us/img207/3690/1291001724centroid.png

    The area is therefore:
    I1=∫(x^2-12x)dx from x=0 to x=12.
    By symmetry, the centroid lies on the line x=6.
    To find the y-distance, evaluate the integral in which each slice is multiplied by y/2=(x^2-12x), equal to the centroid of each slice:
    I2=∫(1/2)(x^2-12x)²dx
    The y-position of the centroid is then:
    yc=I2/I1

    I get yc=-14.4 (below the x-axis)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    could some body please check this for me?
  2. calculus

    A region is bounded by the function y=2x^2+3 and the x-axis over the interval(0,2). Sketch the graph of the bounded region. Use the limit process to find the area of the bounded region. Explain the step in this limit process. Please …
  3. Calculus

    Hi, I need someone to double check my answer because it doesn't seem right to me. Find the centroid of the region bounded by y=0 and y = x^2 -2x. I calculated the area to be 4/3 and centroid (1, 0.4)... is that correct?
  4. Calculus

    Find the centroid of the region bounded by the curve sin x on the interval (0, pi) and the x-axis. Please help
  5. calculus

    find the centroid of the plane region bounded by the curves y = cos x, y=sinx, x=0,
  6. Math61

    R is bounded by Y=2x-x^2 and the x-axis. Find the centroid of R. Sketch the region.
  7. Calculus

    1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where …
  8. calculus

    Find the coordinates of the centroid of the following volume of revolution formed by rotating the area bounded by y^2-4=-x^2, x=0,x=1, And the "x" axis about the "x" axis.
  9. calculus

    3). The shaded region is bounded by the y-axis and the graphs of y=1+√x, y=2. Find the volume of the solid obtained by rotating this region around the x-axis. Answer choices: 7/6pi, 4/3pi, 11/6pi, 5/3pi, 13/6pi, 5/6pi 4). Find …
  10. calculus

    Find the centroid (¯ x, ¯ y) of the region bounded by: y = 6x^2+7x, y = 0, x = 0, and x = 7

More Similar Questions