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Calculus, EXT2 C1 2019 HSC 15c

  1. Show that  .  (2 marks)


  2. Let  .

     


    Show that  .  (3 marks)


  3. Evaluate  .  (2 marks)

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i.   


 

 
 
 
 

 
ii.   

 

 
 
 
 

 

iii.   
 
   
   
   

 

 
 

Calculus, EXT2 C1 2016 HSC 14b

Let    for  

  1. Using a suitable substitution, show that    (3 marks)

  2. Show that    (1 mark)

  3. Find    (3 marks)

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i.  

 

 

 
 
 
 
 
 

 

ii.   
   
   
   
   

 

♦ Mean mark part (iii) 49%.
iii.   
   
   
   
   
   
   
   

Calculus, EXT2 C1 2014 HSC 12d

Let  , where    is an integer and  .

  1. Show that  .  (1 mark)

  2. Show that
     
         .  (2 marks)

  3. Hence, or otherwise, find
     
         .  (2 marks)

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i.   

 
   
 
 

 

♦ Mean mark 41%.
STRATEGY: The denominator of the proof, , should flag the potential existence of in the integral.
ii.  
 

 

 
 
 
 
 

 

iii.