A specialized racing yacht has a structural keel of length 1.8 m. The keel has a symmetrical cross-section as shown in the design specifications, where d d\,d represents the horizontal distance from the center plane and v v\,v represents the vertical depth below the hull waterline, both measured in centimetres. The table below provides the depth profile for one half of the symmetrical cross-section.
d048121620v−18.0−17.65−16.32−13.48−8.550 \begin{array}{|c|c|c|c|c|c|c|}\hline d & 0 & 4 & 8 & 12 & 16 & 20 \\ \hline v & -18.0 & -17.65 & -16.32 & -13.48 & -8.55 & 0 \\ \hline \end{array} dv0−18.04−17.658−16.3212−13.4816−8.55200Use the trapezium rule with all the values in the table to find the best estimate for the total displacement volume of the keel in cm3\text{cm}^3cm3.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
