The diagram includes the line $y = 1$ together with a section of the curve $y = \frac{2}{\sqrt{x+1}}$.
(i)[1]
Show that the equation $y = \frac{2}{\sqrt{x+1}}$ may be rewritten in the form $x = \frac{4}{y^2} - 1$.
(ii)[5]
Evaluate $\int \left( \frac{4}{y^2} - 1 \right) \, dy$. Hence determine the area of the shaded region.
(iii)[5]
The shaded region is rotated through $360^\circ$ around the $y$-axis. Find the exact value of the resulting volume of revolution.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct form is $x=\frac{4}{y^2}-1$.” …
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