Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/23) | Q#4

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Question


i.       
Express  in terms of .

   ii.       Hence show that

Solution

     i.
 

We are given that;

From this we can write;

We have the trigonometric identity;

From this we can write;

Hence;

 

   ii.
 

We are required to show that;

We have found in (i) that;

Therefore;

Rule for integration of  is:

Rule for integration of  is:

Rule for integration of  is:

Rule for integration of  is:

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