The diagram depicts the curve $y = \tan 2x$ for $0 \leq x \leq \frac{\pi}{6}$. The shaded area is enclosed by the curve together with the lines $x = \frac{\pi}{6}$ and $y = 0$.
(i)[3]
Apply the trapezium rule with two intervals to estimate the area of the shaded region, and present your answer correct to 3 significant figures.
(ii)[4]
Determine the exact volume of the solid produced when the shaded region is rotated fully about the $x$-axis.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or indicate the correct $y$-values $0$, $\tan\frac{\pi}{6}$, $\tan^2\!\frac{\pi}{6}$” …