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

\[\int_0^5 f(x) \:dx\]


(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?