The region $R$ is bounded by the curve $y = \frac{x}{x + 1}$ and the lines $y = -x$ and \(x =

Question

The region $R$ is bounded by the curve $y = \frac{x}{x + 1}$ and the lines $y = -x$ and $x = -4$. Find the exact area of $R$. Find the exact volume generated when $R$ is rotated $2\pi$ about the line $x = -4$.

Accepted Answer

(i) $4-\ln3\text{ units}^2$ (ii) $\frac{32\pi}{3}-6\pi\ln3\text{ units}^3$

Applications of Integration - Volume of Revolution about Non-Standard Axes

Applications of Integration - Volume of Revolution about Non-Standard Axes

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