Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 31

 

  Question

A.  Find


i.       


ii.       

 

B.  Use the trapezium rule with 2 intervals to estimate the value of

giving your answer correct to 2 decimal places.

Solution

A.   


i.
 

We are required to find;

Rule for integration of  is:

Rule for integration of  is:

Rule for integration of , or ;


ii.
 

We are required to find;

We know that;

From this we can write;

Therefore;

Rule for integration of  is:

Rule for integration of  is:

Rule for integration of  is:

 

B.   

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;

Comments