The graph displays the curve $y = \sqrt{1 + e^{\frac{1}{3}x}}$ for $0 \leq x \leq 6$. The area enclosed by the curve and the lines $x = 0$, $x = 6$ and $y = 0$ is called $R$.
(i)[3]
Apply the trapezium rule with $2$ strips to estimate the area of $R$, and give your answer accurate to $2$ decimal places.
(ii)[1]
Using the diagram, explain why this estimate is larger than the exact area of $R$.
(iii)[4]
The region $R$ is rotated fully about the $x$-axis. Find 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: “Either state, or clearly indicate, the ordinates $\sqrt{2}$, $\sqrt{1+e}$, $\sqrt{1+e^2}$, or their decimal equivalents” …