The diagram depicts a shaded region enclosed by the $y$-axis, the line $y = -1$, and the section of the curve $y = x^2 + 4x + 3$ for which $x \geq -2$.
(i)[4]
Rewrite $y = x^2 + 4x + 3$ in the form $y = (x + a)^2 + b$, where $a$ and $b$ are constants. Hence, for $x \geq -2$, make $x$ the subject in terms of $y$.
(ii)[6]
Hence, with all necessary working shown, find the volume of the solid produced when the shaded region is rotated through $360^\circ$ about 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: “Gives the inverse relation $y=(x+2)^2-1$” …