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Math Help - finding volume by the washer method

  1. #1
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    finding volume by the washer method

    I have a few problems I'm trying to solve and could use some help on


    1) y=4-x^2, y=2-x (rotate about the x axis)

    So my inner radius is 2-x, my outer radius is 4-x^2

    I integrate from x=-1 to x=3 because that's where they intersect.

    So I integrate:

    pi(4-x^2)^2 - pi(2-x)^2 which comes out to

    48pi - pi4^5/5 + 64pi/3

    2) y= secx, y=tanx, x=0, x=1
    Integrate from 0 to 1, rotate about x axis
    Inner radius is tanx, outer is secx.

    So I have to integrate
    pi(secx)^2 - pi(tanx)^2 = pisec^2x - pitan^2x =

    pi integral sec^2x-sec^2x-1 = -pi(x)


    3)y=2x, y=0, x = 1 (thus x=y/2)
    Rotate about the line x=1

    outside radius = 1-y/2

    integratee pi(1-y/2)^2 which comes out to 2/3pi

    Then I have to do the same shape, but with a different radius (about the line x=2 and limits of integration... so I figure if that one is right then the next one will be too.)
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  2. #2
    MHF Contributor Calculus26's Avatar
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    correct

    you have the right idea on all of them however you may want to consider

    the shell method on #3
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  3. #3
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    Ok great.

    We haven't covered the shell method yet though? My professor mentioned it but didn't go into depth on it yet.
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