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    Taken from P2 Nov. 2004:

    Need to rotate y=4x-(6/x) 2π about the x axis (full circle)

    The answer needs to be exact, im guessing in terms of ln, however when you square the function (before integrating):

    (4x - 6/x)² = (4x - 6/x)(4x - 6/x) giving you what exactly? please help! Thanks
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    π ∫(4x- 6/x)² dx
    = π ∫(16x-24x/x-24x/x+36/x²) dx
    = π ∫(16x-48+36x-2) dx
    = π (16/3 x³ - 48x - 36x-1) + C

    EDIT: I am silly, should have multiplied the integral by pi and not 2pi, sorry!
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    (Original post by Asura)
    Taken from P2 Nov. 2004:

    Need to rotate y=4x-(6/x) 2π about the x axis (full circle)

    The answer needs to be exact, im guessing in terms of ln, however when you square the function (before integrating):

    (4x - 6/x)² = (4x - 6/x)(4x - 6/x) giving you what exactly? please help! Thanks
    (4x - 6/x)² = (4x - 6/x)(4x - 6/x) = 16x2 - 48 + 36x-2 = y2

    => ∫y2dx = ∫16x2 - 48 + 36x-2dx

    => [16/3x3 - 48x - 36x-1]

    Put y = 0, 0 = 4x - 6/x

    => 0 = 4x2 - 6

    => 4x2 = 6

    => x = ±√(3/2)

    Then sub in these values and times by pi.
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    Got it, nice one lads, always think that when they want exact it means logs, just a fixation, thanks again
 
 
 
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Updated: June 19, 2005
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