I get the two intersections at x = (1 - √13)/2, (-1 + √13)/2; let's label them a, b (respectively).
If we evaluate ∫_{a}^{b} π (3 - x^2)^{2} dx (the greater function's volume),
then subtract ∫_{a}^{b} πx^{2} dx (the lesser function's volume),
we get π[9x - 2x^{3} + 1/5 x^{5}]_{a}^{b} - π[1/3 x^{3}]_{a}^{b}
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