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

  1. 👍
  2. 👎
  3. 👁
  1. y = -(x-3)(x-4)

    So, using discs of thickness dx,

    v = ∫[3,4] πr^2 dx
    where r=y
    v = ∫[3,4] π(x^2-7x+12)^2 dx = π/30

    Using shells of thickness dy, and taking advantage of the symmetry,

    v = 2∫[0,1/4] 2πrh dy
    where r=y and h=√(1/4 - y)
    v = 2∫[0,1/4] 2πy√(1/4 - y) dy = π/30

    1. 👍
    2. 👎
  2. A variable force of
    7x−2
    pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from
    x = 1
    ft to
    x = 19
    ft. (Round your answer to two decimal places.)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. 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

  3. Cal 2

    The region bounded by y=3x, y=0, x=3, and x=5 is rotated about the x-axis. Find the volume of the resulting solid.

  4. calculus

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

  1. 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

  2. Calculus

    The region bounded by y=-x^2+14-45 and y=0 is rotated about the y-axis, find the volume.

  3. Calculus

    find the volume of the region bounded by y=e^x, y=0, x=-1, x=1 rotated about the x axis

  4. Cal 2

    Find the volume of the solid whose base is the region bounded by the x-axis, the curves y=x, y=3x^2, x=0, and x=.333333 and which has the property that each cross section perpendicular to the x-axis is an equilateral triangle.

  1. Calculus Help!!

    Region R is bounded by the functions f(x) = 2(x-4) + pi, g(x) = cos^-1(x/2 - 3), and the x axis. a. What is the area of the region R? b. Find the volume of the solid generated when region R is rotated about the x axis. c. Find all

  2. 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,

  3. Math

    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 = −x^2 + 14x − 45, y = 0; about the x-axis

  4. mathematics

    Find the volume V of the solid obtained by rotating the region bounded by curves y=x and y= √𝒙 about the x-axis.

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