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Disc/Washer Method Problem

  1. Jan 26, 2009 #1
    Nevermind, I finally figured it out!


    1. The problem statement, all variables and given/known data

    Find the volume of the solid generated by revolving the region bounded by y=x^1/2 and the lines y=2 and x=0 about:

    a. the x-axis
    b. the y-axis
    c. the line y=2
    d. the line x=4


    2. Relevant equations

    integral from a--b pi[R(x)]^2dx

    integral from a--b pi([R(x)]^2 - [r(x)]^2)dx

    3. The attempt at a solution

    I solved a, b, and c just fine.

    a = 8pi
    b = 32pi/5
    c = 8pi/3

    However I am confused about part d, particularly how to find the radius. The book gives the answer as 224pi/15, but I get 256pi/15.

    I did the following:

    pi*integral from 0 to 2 (4-y^2)^2dy, which gave me 256pi/15 when I worked it out. I may just be messing up the math, though I did the problem a few times the same way and got the same answer every time. I also tried using pi*integral from 0 to 2 16-y^4, but this also yielded the wrong answer. Basically I am not sure how to find the radius of the region it is asking for, when rotating around the line x=4.
     
    Last edited: Jan 26, 2009
  2. jcsd
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