- The table below shows corresponding values of \(x\) and \(y\) for \(y = \log _ { 2 } ( 2 x )\)
The values of \(y\) are given to 2 decimal places as appropriate.
Using the trapezium rule with all the values of \(y\) in the given table,
- obtain an estimate for \(\int _ { 2 } ^ { 14 } \log _ { 2 } ( 2 x ) \mathrm { d } x\), giving your answer to one decimal place.
Using your answer to part (a) and making your method clear, estimate
- \(\quad \int _ { 2 } ^ { 14 } \frac { \log _ { 2 } \left( 4 x ^ { 2 } \right) } { 5 } \mathrm {~d} x\)
- \(\int _ { 2 } ^ { 14 } \log _ { 2 } \left( \frac { 2 } { x } \right) \mathrm { d } x\)
| \(x\) | 2 | 5 | 8 | 11 | 14 |
| \(y\) | 2 | 3.32 | 4 | 4.46 | 4.81 |