CAIE P3 2005 June — Question 2

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2005
SessionJune
TopicArea Under & Between Curves

2
\includegraphics[max width=\textwidth, alt={}, center]{208eab3e-a78c-43b4-918f-a9efc9b4f47a-2_508_586_450_776} The diagram shows a sketch of the curve \(y = \frac { 1 } { 1 + x ^ { 3 } }\) for values of \(x\) from - 0.6 to 0.6 .
  1. Use the trapezium rule, with two intervals, to estimate the value of $$\int _ { - 0.6 } ^ { 0.6 } \frac { 1 } { 1 + x ^ { 3 } } \mathrm {~d} x$$ giving your answer correct to 2 decimal places.
  2. Explain, with reference to the diagram, why the trapezium rule may be expected to give a good approximation to the true value of the integral in this case.