1. Questions

Calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.

  1. 👍
  2. 👎
  3. 👁
Anonymous

  1. V = π∫(y^2) dx from a to b

    = π∫x^4 dx from 0 to 3
    = π[x^5/5] from 0 to 3
    = π(243/5 - 0) = 243π/5 cubic units

    1. 👍
    2. 👎
    Reiny

  2. or, using shells, you can do

    V = ∫[0,9] 2πrh dy
    where r = y and h = 3-x
    = 2π∫[0,9] y(3-√y) dy
    = 2π(3/2 y^2 - 2/5 y^(5/2)) [0,9]
    = 2π(3/2 * 81 - 2/5 * 243)
    = 2π(243/10)
    = 243π/5

    1. 👍
    2. 👎
    Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 8 sin x, y = 8 cos x, 0 ≤ x ≤ π/4; about y = −1

  2. Calculus

    Find the volume of the solid obtained by rotating the region bounded by y= x^(1/3), and y= x about the line y=1

  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 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,

  1. calculus

    Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. xy = 2, x = 0, y = 2, y = 4

  2. cal

    Find the volume of the solid obtained by rotating the region bounded by y=4x^2,x=1,y=0 about the x-axis.

  3. calculus

    Find the volume of the solid obtained by rotating the region bounded by the curves y = x^8, y = 1 about the line y = 5.

  4. calculus

    Find the volume of the solid obtained by rotating the region bounded by y=x and y=√x about the line x=2. Volume =

  1. Calculus 2

    Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=1/x, y=0, x=1 and x=4 about the line y=−1

  2. 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

  3. Calculus

    Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y = 0.5x2 and y = x about the line x = 7. (10 points)

  4. Calc2

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x2, y = 1; about y = 6

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