The region R is bounded by the graph $$y = -x^2+3x$$ and the $x-axis$ revolved about the line $x=4$. Find the volume.
2026-04-05 14:17:03.1775398623
Volume Of Revolution Problem
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Our method is Shell. We have: $y = -x^2+3x$, and the $x$ intercepts are: $0,3$, $r = 4-x \to V = \displaystyle \int_{0}^{3} 2\pi(-x^2+3x)(4-x)dx$
If $3x$ was replaced by $2x$, then our analysis becomes: $V = \displaystyle \int_{0}^{2} 2\pi(-x^2+2x)(4-x)dx$