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Trapezium Rule And Errors Item

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Trapezium Rule and Errors Item 1 Environmental engineers were studying the flow of water through a small irrigation channel. The velocity of water v (in metres per second) was measured at different positions x metres across the width of the channel. The channel is 10 metres wide. The measurements obtained were: x (m): 0, 2, 4, 6, 8, 10 v (m/s): 0.8, 1.2, 1.6, 1.4, 1.1, 0.7 The engineers want to estimate the total discharge across the channel using numerical integration because the exact function for velocity is unknown. Tasks A. Trapezium Rule State the trapezium rule formula for numerical integration. Use the trapezium rule to estimate the value of the integral from x = 0 to x = 10 of v(x) dx. B. Interpretation Explain why the trapezium rule is suitable when dealing with experimental data. State two assumptions made when using the trapezium rule. C. Errors Define absolute error. Define percentage error. If the exact value of the integral is 12.5, calculate the percentage error in your trapezium rule estimate. D. Accuracy Explain how the accuracy of the trapezium rule can be improved. State one limitation of numerical integration in practical measurements. Designed by Tr Joel PCM Designer of Physics, Chemistry and Mathematics Item Banks “Persistence Leads to Success.” [email protected] 0788477510

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