Sasha monitors the rate of water flow RRR (in litres per minute) into a drainage tank during a 12-minute heavy storm. The readings taken from a sensor at 2-minute intervals are recorded in the table below:
t (min)024681012R (L/min)450112024804750510039501850 \begin{array}{|c|c|c|c|c|c|c|c|} \hline t \text{ (min)} & 0 & 2 & 4 & 6 & 8 & 10 & 12 \\ \hline R \text{ (L/min)} & 450 & 1120 & 2480 & 4750 & 5100 & 3950 & 1850 \\ \hline \end{array} t (min)R (L/min)045021120424806475085100103950121850Sasha claims that, during this 12-minute period, the total volume of water that entered the tank is approximately 37,00037,00037,000 litres.
By applying the trapezium rule to all the data in the table, determine if Sasha's estimate is correct to the nearest 1,0001,0001,000 litres. Show your working clearly.
Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only), matched to the AQA A Level Maths (7357) 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.
