Standard +0.8 This is a standard inverse hyperbolic integration requiring recognition of the arccosh form and substitution u=x-5, followed by evaluation at limits. While it requires knowledge of a Further Maths formula and careful algebraic manipulation, it's a direct application of a known result with no novel problem-solving required. The 4-mark allocation and straightforward structure place it slightly above average difficulty.
Find the value of \(\int_6^7 \frac{1}{\sqrt{(x-5)^2-1}} \, dx\), giving your answer in the form \(\ln(a + \sqrt{b})\), where \(a\) and \(b\) are integers to be determined. [4]
Find the value of $\int_6^7 \frac{1}{\sqrt{(x-5)^2-1}} \, dx$, giving your answer in the form $\ln(a + \sqrt{b})$, where $a$ and $b$ are integers to be determined. [4]
\hfill \mbox{\textit{CAIE Further Paper 2 2024 Q1 [4]}}