Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/23) | Q#7

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Question

a)   Find

b)   


i.   
Find


ii.   
Hence find

giving your answer in the form .

Solution

a)    

We are required to find;

Rule for integration of  is:

First we integrate .

From  we can obtain;

Rule for integration of  is:

Rule for integration of  is:

Rule for integration of  is:

Next we integrate .

Rule for integration of  is:

Finally, we integrate .

Rule for integration of  is:

Hence;

b)   


i.
 

We are required to find;

Rule for integration of  is:

First we integrate .

Rule for integration of  is:

Next we integrate .

For ;

Hence;


ii.
 

We are required to find the following in the form .

As demonstrated in (i);

Hence;

Power Rule;

Division Rule;

Power Rule;

Multiplication Rule;

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