Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/22) | Q#7

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  Question

     i.       Show that

   ii.       Solve the equation  for , giving your answers  correct to 3 significant figures.

  iii.       Find

Solution

     i.
 

We are given;

  provided that

  provided that

 

   ii.
 

We are required to solve the equation for .

As demonstrated in (i);

Therefore;

Let ;

Now we have two options.

Since ;

Using calculator;

Now we find all solutions in the interval .

Properties of

Domain

Range

Periodicity

Odd/Even

Translation/

Symmetry

We utilize the periodicity/symmetry property of   to find other solutions (roots) of :  

Therefore;

For ;

For ;

Only following solutions (roots) are within the given interval ;

 

  iii.
 

We are required to find;

As demonstrated in (i);

Therefore;

Hence;

Rule for integration of  is:

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