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.
864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.