SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Calculus, EXT2 C1 2017 HSC 15a

Let  , for  

  1. Find the value of .  (1 mark)

  2. Using integration by parts, or otherwise, show that for  
     
         .  (3 marks)

  3. Find the value of  .  (1 mark)

Show Answers Only
Show Worked Solution
i.  
   
   
   
   

 

ii. 

♦ Mean mark 48%.

   
 
 
 

 

 

iii.  
   
   
   

Calculus, EXT2 C1 2013 HSC 13a

Let  , where    is an integer.

  1. Show that
     
              for every integer    (3 marks)

  2. Evaluate    (2 marks)

Show Answers Only
Show Worked Solution

i. 

♦ Mean mark 46%.
STRATEGY TIP: Attempting to prove this relationship using induction proved unsuccessful and time consuming for some students.
 

 

 
 
 
 
 

 
STRATEGY TIP: Realising that the integral is equal to the area of a quarter unit circle saved valuable time.

 

ii.