9758/2022/P1/Q07

7 A curve $C$ has equation $y=x^{-3} \ln x$.
(a) Show that $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1-3 \ln x}{x^4}$ and hence find the coordinates of the turning point of $C$.

[4]

(b) Find the exact area enclosed by $C$, the $x$-axis and the line $x=3$.

[5]