Question 20

The power output, $P\,$ kW, of a solar array is monitored over a 12-hour period. The graph of $P\,$ against time $t$ (hours after 00:00) shows the system's performance between $t = 8$ and $t = 20$ . Readings taken from the graph at regular 4-hour intervals are recorded in the table below.

\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}

Graph of solar-array power output P in kilowatts against time t from 8 to 20 hours, passing through the four recorded readings.

Use the trapezium rule with three strips of equal width to estimate the total energy produced, in kilowatt-hours (kWh), over the interval $\le t \le 20$ .

It is suggested that the power output $P\,$ can be modelled by a quadratic function of $t\,$ for $\le t \le 20$ . Explain how this model could be used to find an alternative estimate for the total energy produced during this time interval.

\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}

Graph of solar-array power output P in kilowatts against time t from 8 to 20 hours, passing through the four recorded readings.

Use the trapezium rule with three strips of equal width to estimate the total energy produced, in kilowatt-hours (kWh), over the interval $\le t \le 20$ .

11.9 The Trapezium Rule

11.9 The Trapezium Rule Questions

11.9 The Trapezium Rule

Question 20

11.9 The Trapezium Rule Questions