The area bound between $y=0$ and part of the curve $y=\sin (x)$ is sketched below.

1. Using the trapezium rule with $6$ strips, find an approximate value for the area indicated.

2. By drawing a suitable diagram, explain whether this area is an overestimate or an underestimate.

3. State how the accuracy of the approximation may be improved.

For (a), $h=\frac{b-a}{n}=\frac{\frac{\pi }{2}-0}{6}$

For (b), notice that the trapezia don't quite cover the area they're trying to estimate:

This is a much tighter fit between the trapezia and the area:

What have we done here?

Give the approximate area, to $3$ significant figures.