The diagram shows the region ${R}$, which is bounded by the curve ${(y-2)^{2}=2x-3}$ and the lin

Question

The diagram shows the region ${R}$, which is bounded by the curve ${(y-2)^{2}=2x-3}$ and the line ${x=3.5}$. Find the area of region ${R}$. volume when ${R}$ is rotated through four right angles about the ${x}$-axis. volume when ${R}$ is rotated through ${2\pi}$ about the ${y}$-axis.

Accepted Answer

(i) $\frac{16}{3}\text{ units}^2$ (ii) $\frac{64\pi}{3}=67.0\text{ units}^3\text{ (3 s.f.)}$ (iii) $\frac{144\pi}{5}=90.5\text{ units}^3\text{ (3 s.f.)}$

Applications of Integration - Volume of Revolution: Roots of Equations

Applications of Integration - Volume of Revolution: Roots of Equations

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