Challenging +1.2 This is a Further Maths integration question requiring recognition of an inverse hyperbolic form (arsinh) and appropriate substitution. While it requires knowledge beyond standard A-level, the integration is relatively straightforward once the form is identified, and the question provides clear guidance. The 7 marks reflect moderate length but the technique is standard for FP3 students who have learned these forms.
\includegraphics{figure_12}
Figure 1 shows the cross-section \(R\) of an artificial ski slope. The slope is modelled by the curve with equation
$$y = \frac{10}{\sqrt{4x^2 + 9}}, \quad 0 \leq x \leq 5.$$
Given that 1 unit on each axis represents 10 metres, use integration to calculate the area \(R\). Show your method clearly and give your answer to 2 significant figures. [7]
\includegraphics{figure_12}
Figure 1 shows the cross-section $R$ of an artificial ski slope. The slope is modelled by the curve with equation
$$y = \frac{10}{\sqrt{4x^2 + 9}}, \quad 0 \leq x \leq 5.$$
Given that 1 unit on each axis represents 10 metres, use integration to calculate the area $R$. Show your method clearly and give your answer to 2 significant figures. [7]
\hfill \mbox{\textit{Edexcel FP3 Q12 [7]}}