(See Solution) R is the region that lies between the curve y=(1)/(x^2+4 x+5) and the x -axis from x=-3 to x=-1. Find: the area of R, the volume of the solid
Question: \(\mathrm{R}\) is the region that lies between the curve \(y=\frac{1}{x^{2}+4 x+5}\) and the \(x\) -axis from \(x=-3\) to \(x=-1\). Find:
- the area of \(\mathrm{R}\),
- the volume of the solid generated by revolving \(R\) around the \(y\) -axis.
- the volume of the solid generated by revolving \(\mathrm{R}\) round the \(x\) -axis.
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