7.
$$I = \int _ { 2 } ^ { 5 } \frac { 1 } { 4 + \sqrt { } ( x - 1 ) } \mathrm { d } x$$
- Given that \(y = \frac { 1 } { 4 + \sqrt { } ( x - 1 ) }\), complete the table below with values of \(y\) corresponding to \(x = 3\) and \(x = 5\). Give your values to 4 decimal places.
- Use the trapezium rule, with all of the values of \(y\) in the completed table, to obtain an estimate of \(I\), giving your answer to 3 decimal places.
- Using the substitution \(x = ( u - 4 ) ^ { 2 } + 1\), or otherwise, and integrating, find the exact value of \(I\).