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.
137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.