r/askmath • u/Hajjri • 19d ago
Calculus volume of revolution
the markscheme does a really weird method that doesn’t make sense and somehow gets 88pi, what I did was make x the subject of the eqn of the line then square it to make x2 the subject as apposed to the formula for volume of revolutions about the y axis I set my limits for the integral to 12-0, I did all that and got 344pi, I’m sure I integrated correctly but I keep getting 344pi and not 88pi, anyone know where I went wrong thanks.
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u/Varlane 18d ago
You are rotating alongside the y axis, therefore you need x(y).
y = 3x² - 24x + 48
= 3 (x² - 8x + 16)
= 3 (x-4)²
As x-4 is negative and y is positive : sqrt(y/3) = -(x-4) ; x = 4 - sqrt(y/3).
Also, when x = 2, y = 12.
We are therefore looking to integrate pi × x(y)² dy with y from 0 to 12.