Review question

# Can we apply the trapezium rule to $f(x) = x/2 - \lfloor x/2 \rfloor$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8140

## Suggestion

For a real number $x$, we denote by $\lfloor x \rfloor$ the largest integer less than or equal to $x$. Let

$f(x) =\dfrac{x}{2}-\left\lfloor \dfrac{x}{2} \right\rfloor.$

The smallest number of equal width strips for which the trapezium rule produces an overestimate for the integral

$\int_0^5 f(x) \:dx$

is

(a) $2,\quad$ (b) $3,\quad$ (c) $4,\quad$ (d) $5,\quad$ (e) it never produces an overestimate.

Can we sketch the curve?

Can we add to our sketch what happens if we apply the trapezium rule with 2 strips? With 3? With more?