Trapezium Rule

WMA12/01 IAL (Edexcel)/P2/Jan 2021/Q7 (The Trapezium Rule)

Solar panels are installed on the roof of a building.​​ 

The power, P, produced on a particular day, in kW, can be modelled​​ by the equation​​ 

P = 0.95 + 2t-12 + 212-t - t - 122       8.5≤ t ≤ 15.2

where t is the time in hours after midnight. The graph of P against t is shown in Figure 1.​​ 

A table of values of t and P is shown below, with the values of P given to 4 significant figures where appropriate.​​ 

• Use the given equation to complete the table, giving the values of P to 4 significant figures where appropriate.​​ 

(2)​​ 

The amount of energy, in kWh, produced between 10:00 and 12:00 can be found by calculating​​ the area of region R, shown shaded in Figure 1.​​ 

• Use the trapezium rule, with all the values of P in the completed table, to find an estimate for the amount of energy produced between 10:00 and 12:00. Give your answer to 2 decimal places.​​ 

(4)

SOLUTION

a-​​ Using the given equation, to find the values of P for t=10 & t=11.5.

P=0.95+2t-12+212-t-t-122

For​​ t=10,

P=0.95+2-2+22--22=1.2

For​​ t=11.5,

 P=0.95+2-05+20.5--0.52=2.82132 

b-​​ 

Using Trapezium Rule to estimate the area bounded between 10 hours and 12 hours.

(The​​ number of trapezium strips are 4 as we know that the number of strip is always 1 less than the total number of values of x and y given.)

h=b-an=12-104=24=0.5

A=0.2525.453+5+27.764+9.375+9.964+9.367+7.626

A=0.521.2+2.95+21.882+2.45+2.821

A=4.614

A=4.61 kwh