The sketch shows the curve given by $y = \sqrt{(1 + 3\cos^2(\tfrac{1}{2}x))}$ for $0 \le x \le \pi$. The region $R$ lies between the curve, the coordinate axes and the line $x = \pi$.
(i)[3]
Apply the trapezium rule with two intervals to estimate the area of $R$, and give the answer correct to $3$ significant figures.
(ii)[5]
The region $R$ is rotated 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: “Take the $y$-values as $2,\sqrt{2.5},1$ or matching equivalents” …