2022 RI P1 Q8
A curve $C$ is defined by $y=\frac{{{\left( \ln x \right)}^{4}}}{\sqrt{x}}$ where $0<x<10$.
(i)
Find the exact volume generated when the area bounded by $C$, the $x$-axis and the lines $x=1$ and $x=\text{e}$ is rotated about the $x$-axis through ${{360}^{\circ }}$.
[4]
(ii)
Find the area enclosed by $C$ and the lines $y=1$ and $y=\text{e}$.
[6]
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