The question is simple enough, but I am unable to get the correct answer even after multiple tries. I integrate the volume element $pi*x^2*dy$ between y equals [0, -3].
2026-03-26 01:12:11.1774487531
Let R be the region between the curve $y = -(x-2)^2+1$ and the x-axis. Find the volume of the region obtained by revolving R about the y-axis.
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Using vertical slices, the integral is $$\int_{1}^3 2\pi \,r(x)h(x) dx$$ where $$h(x) = -(x-2)^2 + 1$$ and $$r(x) = x$$