calculus

The region R is the region in the first quadrant bounded by the curves y = x^2-4x+4, x=0, and x=2.
Find a value h such that the vertical line x = h divided the region R into two regions of equal area. You get h = ?
I solved for the total area under the curve (8/3) and the area of each half (4/3). How do I get the h value from here?

  1. 👍
  2. 👎
  3. 👁
  1. You are correct in the total area to be 8/3 and half of that would be 4/3
    You also must have had the correct integral to obtain the 8/3
    so just evaluate it from x = 0 to h instead of 0 to 2, then set that equal to 4/3

    that is,
    (1/3)(h^3) -2(h^2) + 4h - 0 = 4/3

    This does not solve easily, unless I made an arithmetic error

    1. 👍
    2. 👎
  2. I think you forgot to include y=0 as part of the boundary,
    and the line x=2 plays no role, since the vertex of the curve is at (2,0)
    So, I'll go on assuming the triangular region bounded by the curve and the x- and y-axes.

    As you say, ∫[0,2] (x^2-4x+4) dx = 8/3
    So now you want
    ∫[0,h] (x^2-4x+4) dx = 4/3
    That means that
    1/3 h^3 - 2h^2 + 4h = 4/3
    h^3-6h^2+12h-4 = 0
    h^3-6h^2+12h-8 = -4
    (h-2)^3 = -4
    h-2 = -∛4
    h = 2-∛4

    1. 👍
    2. 👎
  3. Thanks oobleck, my weakness is not reading questions
    completely.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    1. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = sin(x), y = 0, π/2 ≤ x ≤ π; about the x−axis 2. Find the volume V obtained by rotating the region bounded by the curves

  2. calculus

    1. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(5x), y = 1, y = 3, x = 0; about the y-axis 2. Use the method of cylindrical shells to find the volume V

  3. calculus

    Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips

  4. Calculus

    Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = −3.

  1. calculus

    Find the volume of the solid generated by revolving the region about the given line. The region in the second quadrant bounded above by the curve y = 16 - x2, below by the x-axis, and on the right by the y-axis, about the line x =

  2. calculus

    Let A be the region bounded by the curves y=x^2-6x+8 and y=0, find the volume when A is revolved around the x-axis

  3. K

    Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3e^(-x), y = 3, x = 2; about y = 6

  4. Calculus

    Find the area of the region bounded by the curves y = sin x, y = csc^2x, x = pi/4, and x = (3pi)/4.

  1. Math

    Find the volume of the solid generated by revolving the following region about the given axis The region in the first quadrant bounded above by the curve y=x^2, below by the x-axis and on the right by the line x=1, about the line

  2. calculus

    Find the area of region bounded by the curves y=sin(pi/2*x)and y=x^2-2x.

  3. Calculus

    Find the area of the region bounded by the curves y=12-x^2 and y=x^2-6. Hint:The answer should be a whole number.

  4. calculus review please help!

    1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate,

You can view more similar questions or ask a new question.