Find the volumes of solid formed when region ${R}$ is rotated through ${2\pi}$ about
${y}$-axis,
${x}$-axis.

Question

Find the volumes of solid formed when region ${R}$ is rotated through ${2\pi}$ about ${y}$-axis, ${x}$-axis.

Accepted Answer

(a) $\frac\pi2\left(e^2+3e^{-2}\right)=12.2\text{ units}^3\text{ (3 s.f.)}$ (b) $8\pi\left(e-\frac6e\right)=12.8\text{ units}^3\text{ (3 s.f.)}$

Applications of Integration - Volume of Revolution: Roots of Equations