Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/22) | 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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