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.
125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.