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Volume problem

  1. Jun 2, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the soild formed.
    The region bounded by the line y=x, and the curve y=x^2. about the line x=1

    2. Relevant equations

    Either Washer or Shell

    3. The attempt at a solution

    I want to use washer, but have to switch to dy.
    I want to use shell, but don't think it will work.

    I don't think this is right, but here is what I have.

    integral of pie[(1-y^(1/2))-(1-y)]dy from 0 to 1.

    Thanks, please help.
  2. jcsd
  3. Jun 2, 2007 #2
    Ok for a washer the area is pie(r1^2 - r2^2), where r1 is the larger radius and r2 is the smaller radius. So I think you just need to take a closer look at which is the larger and smaller radius and remember to square them too.

    OTOH if you used shells you might not have to deal with a square root term in your integral.
  4. Jun 2, 2007 #3
    the about x=1 is what mess me up. i meant to spuare all the R's but forgot, because this is hard to see.

    integral of pie[(1-y)^2-(1-y^(1/2))^2]dy from 0 to 1.

    this is right now?

    I got pi/6, it looks right, but is it?
    Last edited: Jun 2, 2007
  5. Jun 3, 2007 #4


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    Looks correct to me.
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