WAEC 2022 · Paper 2 · Q3

(a)
Using the trapezium rule with five ordinates, evaluate, correct to two decimal places, $\displaystyle\int_1^3 \frac{2}{x + 4}\,dx$ .

Worked solution (try it first)

Five ordinates means four strips, so $h = \dfrac{3 - 1}{4} = 0.5$ .
The ordinates of $\dfrac{2}{x + 4}$ at $x = 1, 1.5, 2, 2.5, 3$ are $0.4,\ 0.3636,\ 0.3333,\ 0.3077,\ 0.2857$ .
First and last: $0.6857$ .
Twice the rest: $2(0.3636 + 0.3333 + 0.3077) = 2.0093$ .
Trapezium rule: $\dfrac{0.5}{2}(0.6857 + 2.0093) = 0.25 \times 2.6950$
$= 0.6738$ , about $0.67$ .