Challenging +1.2 This is a volume of revolution problem requiring integration with respect to y (since rotating about y-axis), involving hyperbolic functions and their inverses. Students must rearrange y = cosh(x²/2) to find x² in terms of y, set up the integral πx²dy, and evaluate using substitution with hyperbolic identities. While it requires multiple techniques (inverse hyperbolic functions, substitution, integration), these are standard Further Maths topics and the setup is straightforward once the correct form is identified. The 7-mark allocation reflects moderate length rather than exceptional difficulty.
In this question you must show detailed reasoning.
The region in the first quadrant bounded by curve \(y = \cosh\frac{1}{2}x^2\), the \(y\)-axis, and the line \(y = 2\) is rotated through \(360°\) about the \(y\)-axis.
Find the exact volume of revolution generated, expressing your answer in a form involving a logarithm. [7]
In this question you must show detailed reasoning.
The region in the first quadrant bounded by curve $y = \cosh\frac{1}{2}x^2$, the $y$-axis, and the line $y = 2$ is rotated through $360°$ about the $y$-axis.
Find the exact volume of revolution generated, expressing your answer in a form involving a logarithm. [7]
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q13 [7]}}