A curve $C$ has equation $y={{\mathrm{e}}^{x}}$. Find the exact volume of revolution when the region

Question

A curve $C$ has equation $y={{\mathrm{e}}^{x}}$. Find the exact volume of revolution when the region bounded by $C$, the line $y=3$ and the $y$-axis is rotated completely about the $y$-axis. [5] Describe a pair of transformations which transforms the curve with equation $y={{\mathrm{e}}^{1+2x}}$ on to the curve $C$. [2]

Accepted Answer

(a) $\pi\left[3(\ln 3)^2 - 6\ln 3 + 4\right]$ units³; (b) Scale by 2 parallel to x-axis, then translate 1 unit in +x direction

2019 NJC Promo Q4

2019 NJC Promo Q4

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