The diagram illustrates a section of the curve with equation $y = \sqrt{x^3 + x^2}$. The shaded area is enclosed by the curve, the $x$-axis and the line $x = 3$.
(i)[4]
Find, showing all the required working, the volume produced when the shaded region is turned through $360^\circ$ about the $x$-axis.
(ii)[6]
$P$ is the point on the curve with $x$-coordinate $3$. Find the $y$-coordinate of the point where the normal to the curve at $P$ crosses the $y$-axis.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the volume of revolution formula $V=\pi\int(x^3+x^2)\,dx$” …