Challenging +1.8 This is a challenging Further Maths integration question requiring knowledge that 1/cosh(u) = sech(u), the substitution t = tanh(u) or equivalent manipulation using exponential definitions, and evaluation of an improper integral. While the techniques are standard for FM students, the combination of hyperbolic functions, improper integrals, and requirement for exact form without calculator makes this significantly harder than average A-level questions.
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
Find
$$\int_1^{\infty} \frac{1}{\cosh u} du,$$
giving your answer in an exact form.
[7 marks]
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
Find
$$\int_1^{\infty} \frac{1}{\cosh u} du,$$
giving your answer in an exact form.
[7 marks]
\hfill \mbox{\textit{SPS SPS FM 2021 Q6 [7]}}