Review question

Ref: R5642

## Suggestion

The graph $y=f(x)$ of a function is drawn below for $0 \le x \le 1$.

The trapezium rule is then used to estimate

$\displaystyle\int_0^1 \! f(x) \, \mathrm{d}x$

by dividing $0 \le x \le 1$ into $n$ equal intervals. The estimate calculated will equal the actual integral when

1. $n$ is a multiple of $4$;

2. $n$ is a multiple of $6$;

3. $n$ is a multiple of $8$;

4. $n$ is a multiple of $12$.

The notation $\displaystyle\int_0^1 \! f(x) \, \mathrm{d}x$ means the area between the $f(x)$ and the $x$-axis, from $x=0$ to $x=1$.