The power output, P P\,P kW, of a solar array is monitored over a 12-hour period. The graph of P P\,P against time ttt (hours after 00:00) shows the system's performance between t=8t = 8t=8 and t=20t = 20t=20. Readings taken from the graph at regular 4-hour intervals are recorded in the table below.
t8121620P1.26.85.40.6 \begin{array}{|c|c|c|c|c|} \hline t & 8 & 12 & 16 & 20 \\ \hline P & 1.2 & 6.8 & 5.4 & 0.6 \\ \hline \end{array} tP81.2126.8165.4200.6
Use the trapezium rule with three strips of equal width to estimate the total energy produced, in kilowatt-hours (kWh), over the interval 8≤t≤208 \le t \le 208≤t≤20.
It is suggested that the power output P P\,P can be modelled by a quadratic function of t t\,t for 8≤t≤208 \le t \le 208≤t≤20. Explain how this model could be used to find an alternative estimate for the total energy produced during this time interval.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) 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.
