The function $f$ is defined by

The curve $y=f(x)$ is sketched below:

1. Use the trapezium rule with $4$ strips to find an approximate value for the area $A$

2. Use the area $A$ to find an approximate value for the area $B$

3. Approximate $B$ in a different way, by using the trapezium rule with $4$ strips to estimate

   $${\int }_a^b{f}^{-1}(y)dy$$

   for appropriate values of $a$ and $b.$

4. Explain, by drawing an appropriate diagram, why the estimates given in (b) and (c) are not identical.

Give the absolute value of the difference between the estimates found in (b) and (c), correct to $3$ significant figures.