Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2013  OctNov  (P29709/22)  Q#6
Hits: 75
Question
A. Find
B.
i. Use the trapezium rule with 2 intervals to estimate the value of
giving your answer correct to 3 decimal places.
ii. Using a sketch of the graph of for , explain whether the trapezium rule gives an underestimate or an overestimate of the true value of the integral in part (i).
Solution
A.
We are required to find;
We have formula;
We have the trigonometric identity;
Therefore;
We know that;
Therefore;
Hence;
Rule for integration of is:
Rule for integration of is:
Rule for integration of is:
B.
i.
We are required to apply Trapezium Rule to evaluate;
The trapezium rule with intervals states that;
We are given that there are two intervals, .
We are also given that and .
Hence;




1 



2 



3 


Therefore;
ii.
We know that graph of is as shown below.
However, we are only interested in for the interval . Therefore;
If the graph is bending upwards over the whole interval from to , then trapezium rule will give an overestimate of the true area.
It is evident that for the given graph trapezium rule will give an overestimate.
Comments