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\includegraphics[max width=\textwidth, alt={}, center]{6295873e-7db4-4e7e-8dcd-912ad9c41675-06_561_542_260_799}
The diagram shows the curve \(y = \tan 2 x\) for \(0 \leqslant x \leqslant \frac { 1 } { 6 } \pi\). The shaded region is bounded by the curve and the lines \(x = \frac { 1 } { 6 } \pi\) and \(y = 0\).
- Use the trapezium rule with two intervals to find an approximation to the area of the shaded region, giving your answer correct to 3 significant figures.
- Find the exact volume of the solid formed when the shaded region is rotated completely about the \(x\)-axis.