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Math Help - Volume

  1. #1
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    Volume

    Volume between these 2 curves

    y = cos(x) and y = 1/2

    a) revolve around the line x= -1
    b) revolve around the line y = 2
    from 0 to pi/6

    I dont know how to set it up.
    Last edited by larryboi7; March 4th 2010 at 10:02 PM.
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  2. #2
    Newbie blackcompe's Avatar
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    Volume between these 2 curves

    y = cos(x) and y = 1/2

    a) revolve around the line x= -1
    b) revolve around the line y = 2
    from 0 to pi/6

    I dont know how to set it up.
    a)

    Using volume by shells you have:

    π = pi
    V = ⌠ 2πx(f(x)-g(x))dx, where I = [a,b]

    Visually, you can see f(x) is cos(x). f(x) and g(x) are the upper and lower boundaries of x, respectively. For each cross section, x represents the radius of the shell that's created by it's revolution about some axis. Generally, that line is the y-axis (x = 0), but it's x = -1, so x becomes (x+1).

    V = 2π⌠(x+1)(cos(x)-(1/2))dx, where I = [0, π/6]

    b)

    Apply the same principles here.
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  3. #3
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    for b) is it the washer method?
    Quote Originally Posted by blackcompe View Post
    a)

    Using volume by shells you have:

    π = pi
    V = ⌠ 2πx(f(x)-g(x))dx, where I = [a,b]

    Visually, you can see f(x) is cos(x). f(x) and g(x) are the upper and lower boundaries of x, respectively. For each cross section, x represents the radius of the shell that's created by it's revolution about some axis. Generally, that line is the y-axis (x = 0), but it's x = -1, so x becomes (x+1).

    V = 2π⌠(x+1)(cos(x)-(1/2))dx, where I = [0, π/6]

    b)

    Apply the same principles here.
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