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# Pure 2 / Core 4 Volumes of Revolution watch

1. 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):

2. 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!
3. (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) = 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.
4. Got it, nice one lads, always think that when they want exact it means logs, just a fixation, thanks again

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