The Trapezium Rule

The speed, $v\,$ m s $^{-1}$ , of a train at time $t\,$ seconds is given by

\sqrt{1.2^t - 1}, \quad 0 \leq t \leq 30.

The following table shows the speed of the train at 5 second intervals.

a.

Complete the table, giving the values of $v\,$ to 2 decimal places.

$t$	0	5	10	15	20	25	30
$v$	0	1.22	2.28		6.11

[3]

b.

The distance, $s\,$ metres, travelled by the train in 30 seconds is given by

\int_0^{30} \sqrt{1.2^t - 1} \, dt.

Use the trapezium rule, with all the values from your table, to estimate the value of $s$ .

[3]

The speed, $v\,$ m s $^{-1}$ , of a train at time $t\,$ seconds is given by

\sqrt{1.2^t - 1}, \quad 0 \leq t \leq 30.

The following table shows the speed of the train at 5 second intervals.

a.

Complete the table, giving the values of $v\,$ to 2 decimal places.

$t$	0	5	10	15	20	25	30
$v$	0	1.22	2.28		6.11

[3]

b.

The distance, $s\,$ metres, travelled by the train in 30 seconds is given by

\int_0^{30} \sqrt{1.2^t - 1} \, dt.

Use the trapezium rule, with all the values from your table, to estimate the value of $s$ .

[3]

The Trapezium Rule Questions