Calculus

posted by .

Using the Disk Method or washer method (im not sure which one)
Find The volume of y=x^3 , y=1 , x = 2
revolving around the X axis

  • Calculus -

    V=PI*INT y^2 dx
    =PI INT x^6 dx from x=1 to x=2

    PI*y^2 is the area of the disk
    dx is its thickness.

  • Calculus -

    I will assume you want to rotate the region bounded by your three curves.

    vol = π(integral) (x^6 - 1)dx
    = π[(x^7)/7 - x]from 1 to 2
    = pi[128/7-2 - (1/7 - 1)]
    = π[127/7 - 1) cubic units

    check my arithmetic, I have been making some silly typing errors lately.

  • Calculus -

    Maybe you mean the area between the horizontal line y = 1 and the curve y = x^3 from their intersection at (1,1) to the vertical line x = 2 spun around the x axis?
    That would be washers.
    inner radius = 1
    outer radius = x^3
    area of washer = pi (x^3)^2 - pi
    = pi (x^6-1)
    integrate that times dx from x = 1 to x = 2
    pi ( x^7/7 - x) at x = 2 = pi 128/7 -14/7) = pi (114/7)
    pi (x^7/7 - x) at x = 1 = pi(1/7 - 1)= pi (-6/7)
    so
    pi (120/7)

  • Calculus -

    Well, we check this time :)

  • Calculus -

    noticed that too, lol

    but, after all, I am on third cup of coffee.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    find the volume of the solid formed by revolving the region bounded by the graphs of y=x^3,y=1, and x=2 about the x-axis using the disk method. 9 express the answer in terms of pie) i got the answer to be 3/5 pie but im not sure if …
  2. calc

    find the volume of the solid generated by revolving around the x-axis: y=e^(x-8), y=0, x=0, x=10 So I know you can use the washer method, but the shell method can also be used and it should be better. The issue is I'm not certain how …
  3. Calculus - Volume by Integration

    Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the y-axis: y=(x-2)^3-2, x=0, y=25 (a)solve by either the disk or washer method (b)solve by the shell method (c)state which …
  4. Calculus - Volume By Integration

    Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the y-axis: y=(x-2)^3-2, x=0, y=25 Solve by either the disk or washer method. I calculated the volume using the shell method …
  5. Urgent Math

    Suppose the area under y = -x^2+1 between x = 0 and x = 1 is rotated around the x-axis. Find the volume by using Disk method and shell method.
  6. Calculus

    I would like to know if my answers are correct: Disclaimer: We are allowed to keep our answers in formula form 1. Use the washer method to find the volume of the solid that is generated by rotating the plane region bounded by y=x^2 …
  7. Calculus

    The region enclosed by the graph e^(x/2), y=1, and x=ln(3) is revolved around the x-axis. Find the volume of the solid generated. I don't understand if we have to use the washer method or the disk method for this one because when I …
  8. Calculus

    The region enclosed by the graph e^(x/2), y=1, and x=ln(3) is revolved around the x-axis. Find the volume of the solid generated. I don't understand if we have to use the washer method or the disk method for this one because when I …
  9. Calculus II: Finding the volume of a revolution

    Question: Find the volume of revolution bounded by y-axis, y=cos(x), and y=sin(x) about the horizontal axis. Since the rotation is happening at the horizontal axis, I thought the limits of integration would be [-1,1] and if the curves …
  10. Math - Calculus

    Find the volume of the solid given by rotating the region bounded by the curves y=x^2, x=1, x=2, and y=0 around the y-axis a) Use the shell method b) Use the washer method. Be careful with the radius of the washer at different y.

More Similar Questions