3.
\includegraphics[max width=\textwidth, alt={}, center]{faa66f88-9bff-4dc9-955f-80cdab3fdd34-1_474_863_1283_520}
The diagram shows the curve with equation \(y = \frac { 4 x } { ( x + 1 ) ^ { 2 } }\).
The shaded region is bounded by the curve, the \(x\)-axis and the line \(x = 1\).
- Use the trapezium rule with four intervals, each of width 0.25 , to find an estimate for the area of the shaded region.
- State, with a reason, whether your answer to part (a) is an under-estimate or an over-estimate of the true area.