The trapezium rule, with the table below, was used to estimate the area between the curve \(y = \sqrt { x ^ { 3 } + 1 }\), the lines \(x = 1 , x = 3\) and the \(x\)-axis.
| \(x\) | 1 | 1.5 | 2 | 2.5 | 3 |
| \(y\) | 1.414 | 2.092 | 3.000 | | |
- Calculate, to 3 decimal places, the values of \(y\) for \(x = 2.5\) and \(x = 3\).
- Use the values from the table and your answers to part (a) to find an estimate, to 2 decimal places, for this area.