Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2019  MayJun  (P29709/22)  Q#4
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Question
a. Find the exact value of
Show all necessary working.
b. Use the trapezium rule with two intervals to find an approximation to
Solution
a.
We are required to show;
We know that , therefore;
Rule for integration of is:
Rule for integration of is:
Rule for integration of is:
Rule for integration of is:
b.
We are required to approximate following using trapezium rule with two intervals;
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;
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