- The table below shows corresponding values of \(x\) and \(y\) for
$$y = 2 ^ { 5 - \sqrt { x } }$$
The values of \(y\) are given to 3 decimal places.
| \(x\) | 5 | 5.5 | 6 | 6.5 | 7 |
| \(y\) | 6.792 | 6.298 | 5.858 | 5.466 | 5.113 |
Using the trapezium rule with all the values of \(y\) in the given table,
- obtain an estimate for
$$\int _ { 5 } ^ { 7 } 2 ^ { 5 - \sqrt { x } } \mathrm {~d} x$$
giving your answer to 2 decimal places.
- Using your answer to part (a) and making your method clear, estimate
- \(\quad \int _ { 5 } ^ { 7 } 2 ^ { 6 - \sqrt { x } } \mathrm {~d} x\)
- \(\int _ { 5 } ^ { 7 } \left( 3 + 2 ^ { 5 - \sqrt { x } } \right) \mathrm { d } x\)