2.
$$y = \frac { x } { \sqrt { ( 1 + x ) } }$$
- Complete the table below with the value of \(y\) corresponding to \(x = 1.3\), giving your answer to 4 decimal places.
| \(x\) | 1 | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 |
| \(y\) | 0.7071 | 0.7591 | 0.8090 | | 0.9037 | 0.9487 |
- Use the trapezium rule, with all the values of \(y\) in the completed table, to obtain an approximate value for
$$\int _ { 1 } ^ { 1.5 } \frac { x } { \sqrt { } ( 1 + x ) } \mathrm { d } x$$
giving your answer to 3 decimal places.
You must show clearly each stage of your working.