Review question

Can we approximate the area under this sine curve? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7912

Question

Draw the graph of $y = \sin x$ for $0 \leq x \leq \pi$, plotting points with $x$-coordinates at intervals of $\dfrac{\pi}{6}$, and labelling them $O, A, B, C, D, E, F$ successively.

Calculate the area of the polygon $OABCDEF$ by dividing it into strips parallel to the $y$-axis, or otherwise. Hence give an approximation to $\int_0^{\pi/2}\sin x \:dx.$