The sketch displays the curve with equation $y = \sqrt{1 + 3\cos^2\left(\tfrac{1}{2}x\right)}$ for $0 \leq x \leq \pi$. The region $R$ is enclosed by the curve, the axes and the line $x = \pi$.
(i)[3]
Apply the trapezium rule with two intervals to estimate the area of $R$, and give your answer correct to $3$ significant figures.
(ii)[5]
The region $R$ is turned fully about the $x$-axis. Without using a calculator, determine the exact volume of the solid formed.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $y$ values $2, \sqrt{2.5}, 1$ or equivalent values” …