CAIE P2 2009 June — Question 3

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2009
SessionJune
TopicIndefinite & Definite Integrals

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 .
  1. 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.
  2. 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).