calculus help

posted by Christine

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
x = 4(square root of (3y)), x = 0, y = 3;
about the y-axis

V=?????

  1. Steve

    x=4√(3y)
    x^2 = 48y

    To use discs, note that the radius of each disc is x, and the thickness is dy, so

    v = ∫[0,3] πx^2 dy
    = 48π∫[0,3] y dy
    = 216π

    To use shells, each shell has radius x, and height 3-y, so

    v = ∫[0,12] 2πx(3-y) dx
    = 2π∫[0,12] x(3-x^2/48) dx
    = 216π

Respond to this Question

First Name

Your Answer

Similar Questions

  1. calculus edit

    1. Find the volume formed by rotating the region enclosed by x=5y and x=y^3 with y is greater than or equal to 0 about the y-axis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the …
  2. calculus

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^4, y=0, x=2, x=9; about y=–5
  3. 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
  4. calculus

    find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. sketch the region and a typical disk or washer. y^2=x, x=2y; about the y-axis i am confused because i do not know how …
  5. Calculus I don't understand

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2, x …
  6. calculus help

    Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4 − 1/2x, y = 0, x = 0, x = 1; about the x-axis V = ?
  7. Calculus Help Please Urgent!!!

    Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x^2, y = 5x, x ≥ 0; about the x-axis V = ?
  8. calculus 2

    Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3x^4, y = 3x, x ≥ 0; about the x-axis
  9. calculus

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x+y = 3, x = 4−(y−1)^2; about the y-axis.
  10. Calculus

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2,y=1; about y=7

More Similar Questions