WAEC 2023 · Paper 2 · Q2

Using the trapezium rule with five ordinates, evaluate, correct to two decimal places, $\displaystyle\int_0^2 \frac{4}{1 + x^2}\,dx$ .

Plot the curves, move them, and read values off the graph.

Worked solution (try it first)

Five ordinates means four strips, so $h = \dfrac{2 - 0}{4} = 0.5$ .
The ordinates of $\dfrac{4}{1 + x^2}$ at $x = 0, 0.5, 1, 1.5, 2$ are $4,\ 3.2,\ 2,\ 1.2308,\ 0.8$ .
First and last: $4.8$ .
Twice the rest: $2(3.2 + 2 + 1.2308) = 12.8615$ .
Trapezium rule: $\dfrac{0.5}{2}(4.8 + 12.8615) = 0.25 \times 17.6615$
$= 4.4154$ , about $4.42$ .