- A continuous curve has equation \(y = \mathrm { f } ( x )\).
The table shows corresponding values of \(x\) and \(y\) for this curve, where \(a\) and \(b\) are constants.
| \(x\) | 3 | 3.2 | 3.4 | 3.6 | 3.8 | 4 |
| \(y\) | \(a\) | 16.8 | \(b\) | 20.2 | 18.7 | 13.5 |
The trapezium rule is used, with all the \(y\) values in the table, to find an approximate area under the curve between \(x = 3\) and \(x = 4\)
Given that this area is 17.59
- show that \(a + 2 b = 51\)
Given also that the sum of all the \(y\) values in the table is 97.2
- find the value of \(a\) and the value of \(b\)