WAEC 2018 · Paper 2 · Q2

Integration

Using the trapezium rule with ordinates at $x = 1, 2, 3, 4$ and $5$ , calculate, correct to two decimal places, the value of $\displaystyle\int_1^5 \left(x + \frac{2}{x^2}\right)dx$ .

(a)
Approximate value

Try it on a graph

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

Worked solution (try it first)

Four strips, $h = 1$ .
The ordinates of $x + \dfrac{2}{x^2}$ at $x = 1, 2, 3, 4, 5$ are $3,\ 2.5,\ 3.2222,\ 4.125,\ 5.08$ .
First and last: $3 + 5.08 = 8.08$ .
Twice the rest: $2(2.5 + 3.2222 + 4.125) = 19.6944$ .
Trapezium rule: $\frac12(8.08 + 19.6944) = 13.8872$ , about $13.89$ .

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