The curve drawn in the diagram is given by the equation $y = \sqrt{1 + e^{0.5x}}$. The shaded area lies between the curve and the lines $x = 0$, $x = 6$ and $y = 0$.
(a)[3]
Apply the trapezium rule with three intervals to estimate the area of the shaded region. State your answer correct to $3$ significant figures.
(b)[4]
The shaded area is turned fully about the $x$-axis. Find the exact volume of the solid formed.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Take the $y$-values $\sqrt{2}$, $\sqrt{1+e}$, $\sqrt{1+e^2}$, $\sqrt{1+e^3}$” …