8. The finite region \(R\) is bounded by the curve \(y = 1 + 3 \sqrt { x }\), the \(x\)-axis and the lines \(x = 2\) and \(x = 8\).
- Use the trapezium rule with three intervals, each of width 2 , to estimate to 3 significant figures the area of \(R\).
- Use integration to find the exact area of \(R\) in the form \(a + b \sqrt { 2 }\).
- Find the percentage error in the estimate made in part (a).