3
\includegraphics[max width=\textwidth, alt={}, center]{b9556031-871d-4dd3-9523-e3438a41339f-2_451_775_559_683}
The diagram shows the curve \(y = \frac { 1 } { 1 + \sqrt { } x }\) for values of \(x\) from 0 to 2 .
- Use the trapezium rule with two intervals to estimate the value of
$$\int _ { 0 } ^ { 2 } \frac { 1 } { 1 + \sqrt { } x } \mathrm {~d} x$$
giving your answer correct to 2 decimal places.
- State, with a reason, whether the trapezium rule gives an under-estimate or an over-estimate of the true value of the integral in part (i).