Post a New Question

Calculus

posted by .

Revolve the region bounded by y=x and y=x^2 about the y axis. In cubic units, the resulting volume is?

  • Calculus -

    You can use discs, integrating along y:

    V = Int(pi (R^2 - r^2) dy)[0,1]
    where R = y and r = sqrt(y)
    = pi*Int(y - y^2)dy[0,1]
    = pi(1/2 y^2 - 1/3 y^3)[0,1]
    = pi(1/2 - 1/3)
    = pi/6

    Or, you can use shells, integrating along x:

    V = Int(2pi*r*h dx)[0,1]
    where r = x h = x-x^2
    = 2pi*Int(x(x-x^2) dx)[0,1]
    = 2pi(x^2 - x^3 dx)[0,1]
    = 2pi(1/3 x^3 - 1/4 x^4)[0,1]
    = 2pi(1/3 - 1/4)
    = 2pi(1/12)
    = pi/6

  • Calculus -

    Revolve the region bounded by y = 4x and y = x2 about the y-axis. In cubic units, the resulting volume is

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus 2

    The region bounded by y=e^(-x^2),y=0 ,x=0 ,x=1 and is revolved about the y-axis. Find the volume of the resulting solid.
  2. calculus

    Is it possible to find an example of a bounded region in the x, y plane that satisfies the following condition : when you revolve the region about the x axis you obtain a solid that has a volume equals its surface area
  3. calculus

    Is it possible to find an example of a bounded region in the x, y plane that satisfies the following condition : when you revolve the region about the x axis you obtain a solid that has a volume equals its surface area
  4. Calculus

    Let R be the region bounded by the x-axis, x = 5 and the curve y = x. This region is rotated around the x-axis. Find the volume of the resulting solid. (Note: R is a triangular region. The resulting solid has a simple shape. You may …
  5. Calculus

    Let R be the square region bounded by y = 2, x = 2, and the x and y-axes. When R is rotated about the x-axis, what is the volume of the resulting solid?
  6. Math

    Revolve the region bounded by y = 4x and y = x^2 about the y-axis. In cubic units, the resulting volume is
  7. Calculus [rotation of region bounded by curves]

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=3x^2, x=1, y=0 about the x-axis
  8. Calculus

    The region in the first quadrant bounded by y=6x^2 , 2x+y=8, and the y-axis is rotated about the line x=-1. The volume of the resulting solid is:
  9. calculus

    The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −x2 + 7x − 12, y = 0; about the x-axis
  10. 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, the …

More Similar Questions

Post a New Question