3. A student tests the accuracy of the trapezium rule by evaluating \(I\), where
$$I = \int _ { 0.5 } ^ { 1.5 } \left( \frac { 3 } { x } + x ^ { 4 } \right) \mathrm { d } x$$
- Complete the student's table, giving values to 2 decimal places where appropriate.
| \(x\) | 0.5 | 0.75 | 1 | 1.25 | 1.5 |
| \(\frac { 3 } { x } + x ^ { 4 }\) | 6.06 | 4.32 | | | |
- Use the trapezium rule, with all the values from your table, to calculate an estimate for the value of \(I\).
- Use integration to calculate the exact value of \(I\).
- Verify that the answer obtained by the trapezium rule is within \(3 \%\) of the exact value.