The diagram depicts the curve $y = x^{\frac{1}{2}} \ln x$. The shaded area bounded by the curve, the $x$-axis and the straight line $x = e$ is labelled $R$.
(i)[4]
Determine the equation of the tangent to the curve at the point where $x = 1$, and express your answer in the form $y = mx + c$.
(ii)[7]
Use integration to find the volume of the solid formed when the region $R$ is turned fully about the $x$-axis. Give your answer in terms of $\pi$ and $e$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the correct product rule” …