Post a New Question

Calculus

posted by .

The area is bounded by y= x^3, x= 2 is rotated around the x-axis. Find the volume using calculus.

  • Calculus -

    I will assume that the x-axis was the other boundary of the region we are rotating

    Using discs ...
    radius = y = x^3

    volume = π∫ y^2 dx from 0 to 2
    = π∫ x^6 dx from 0 to 2
    = π[ (1/7)x^7 ] from 0 to 2
    = π((1/7)(2^7) - 0 ]
    = 128π/7

  • Calculus -

    It is not clear to me how you would do this without using calculus :)

    Graph a sketch of it first. The corners are at (0,0) , (2,0) and (2,8)
    Lets add up a bunch of thin cylinders with axes along x axis
    volume of thin cylinder = pi y^2 dx
    so
    in from x = 0 to x = 2 of pi (x^3)^2 dx

    or pi x^6 dx

    or pi (1/7)x^7
    or 1/7 (128)
    about 18.3

  • times pi -

    I forgot to multiply by pi

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Find the volume of the solid formed when the area bounded by x^2-y^2=9, y=x+5, and the x axis is rotated about x=1.
  2. Calculus

    Let R be the region bounded by y=6sin((pi/2)x), y=6(x-2)^2, y=3x+3 containing the point (2,6). Find the area of R, find the volume of R rotated about the x-axis, find the volume of R rotated about the y-axis, and Suppose R is the base …
  3. 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 …
  4. Calculus

    The area bounded by the curve y = 2x^2-x^3 and line y=0 is rotated around the y-axis. The volume of the resulting structure can be expressed as V = a(pi)/b, where a and b are coprime positive integers. What is the value of a + b?
  5. Calculus

    We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please?
  6. Calculus

    We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please?
  7. calculus

    The area bounded by the curve 2y^2=x and the line 4y=x is rotated around the y-axis. The volume of the resulting structure can be expressed as V=a/bπ, where a and b are coprime positive integers. What is the value of a+b?
  8. calculus

    The area bounded by the curve 2y^2=x and the line 4y=x is rotated around the y-axis. The volume of the resulting structure can be expressed as V=a/bπ, where a and b are coprime positive integers. What is the value of a+b?
  9. calculus

    Set up the simplified integral and compute the volume created when the area bounded by one period of the function 3+sin(x) and the x-axis (use the endpoints of the period starting at x=0) is rotated around: a) the x-axis b) the y-axis
  10. calculus 1

    Set up the simplified integral and compute the volume created when the area bounded by y=.25x4, y=4, and the y=axis (Quadrant 1) is rotated around the line x=-2

More Similar Questions

Post a New Question