The region, , is bounded by the curves    and the line    as shown in the diagram.
 

Find the area of the region .   (3 marks)

Consider the functions    and  , and the regions shaded in the diagram below. 
 

Which of the following gives the total area of the shaded regions?

The diagram shows the graphs of the functions and .
 

It is known that

What is the area between the curves    and    between and ?

1. 5
2. 7
3. 9
4. 11

The region enclosed by    and    is shaded in the diagram.
 

Find the exact value of the area of the shaded region.  (3 marks)

1. Sketch the region bounded by the curve    and the lines    and  .  (1 mark)
   

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2. Calculate the area of this region.  (3 marks)
   

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i.  Show that  .   (2 marks)

ii. 
       
 
Hence, find the area bounded by the graph of    shown above, the -axis and the lines    and  .   (4 marks)