1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integrals and The Washer Method

  1. Jan 18, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid using The Washer Method

    [tex]y=x^2, x=2[/tex]

    2. Relevant equations

    3. The attempt at a solution

    I can solve this problem fine and I don't think my actual question even affects the solution, but I would like to know how one does this.

    In my text book they say to setup the problem on a graph, no problem there. But I am confused on how one obtains the inner line segment.

    Actually here is a drawing since I can't explain what I am looking for.


    How do you find that red line segment? I would think that would matter in the solution, but it doesn't seem to - at least at my level.
  2. jcsd
  3. Jan 18, 2010 #2


    Staff: Mentor

    The length of the red line segment is 2 - sqrt(y), which is the difference of the larger x value (2) and the smaller x value (sqrt(y)).

    You haven't described the region whose volume you want to find. Is the area you show to be revolved around the x-axis or the y-axis, or even some other line?

    From the red line segment you show, it would seem that your region is being revolved around the y-axis.
  4. Jan 18, 2010 #3
    Actually let me ask a real problem question. My prof failed to teach any of this to us, so I am having to learn this on my own.

    Here is the problem.

    The region in the first quadrant is bounded on the left by the circle [tex]x^2 + y^2 =3[/tex], on the right by the line x=sqrt(3), and above by the line y=sqrt(3).

    I can draw the picture fine, but I don't understand to figure out R(x) and r(x) to solve. Any hints so I can get it setup?

    Object is revolving about the y-axis.
  5. Jan 18, 2010 #4
    Got it. And yes it is revolving around the y-axis. I didn't know anything about the red line except it was placed there in my answer book. :)
  6. Jan 18, 2010 #5


    Staff: Mentor

    Each washer has a volume of pi(R(x)^2 - r(x)^2)*delta_y,
    [tex]\Delta V = \pi[(R(x)^2 - r(x)^2]\Delta y[/tex]
    where R(x) = sqrt(3) and r(x) = sqrt(3 - y^2).

    Your washers extend from y = 0 to y = sqrt(3).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook