Finding the volume of revolution of the curve r=2+3cosθ about the initial line?

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]So what I've done is take find the derivative of r wrt θ and use that in the equation for volume,

i.e volume of revolution = $$ \int{2\over 3} r^3 sinθ dθ$$

after substituting $ t=2+3cosθ $ I get $$ \int{2\over 3} {t^3\over-3} dt$$

with the limits from 0 to π in the first case and 5 to -1 in the second case I get the answer as ${104π\over 3}$

Am I doing this right? I feel like there's something really wrong here. Thanks in advance!