The table below shows corresponding values of \(x\) and \(y\) for \(y = \frac { 1 } { \sqrt { ( x + 1 ) } }\), with the values
for \(y\) rounded to 3 decimal places where necessary.
\(x\)
0
3
6
9
12
15
\(y\)
1
0.5
0.378
0.316
0.277
Complete the table by giving the value of \(y\) corresponding to \(x = 15\)
Use the trapezium rule with all the values of \(y\) from the completed table to find an approximate value for
$$\int _ { 0 } ^ { 15 } \frac { 1 } { \sqrt { ( x + 1 ) } } \mathrm { d } x$$
giving your answer to 2 decimal places.