Calculus, EXT1 C2 2006 HSC 1a Find `int (dx)/(49 + x^2).` (2 marks) Show Answers Only `1/7 tan^-1\ x/7 + c` Show Worked Solution `int (dx)/(49 + x^2)` `= 1/7 tan^-1\ x/7 + c`
Calculus, EXT1 C2 2005 HSC 1a Find `int 1/(x^2 + 49)\ dx.` (1 mark) Show Answers Only `1/7\ tan^-1\ x/7 + c` Show Worked Solution `int 1/(x^2 + 49)\ dx` `= 1/7 int 7/(x^2 + 7^2)\ dx` `= 1/7\ tan^-1\ x/7 + c`
Calculus, EXT1 C2 2012 HSC 11a Evaluate `int_0^3 1/(9 + x^2)\ dx`. (3 marks) Show Answers Only `pi/12` Show Worked Solution `int_0^3 1/(9 + x^2)\ dx` `= int_0^3 1/(3^2 + x^2)\ dx` `= [1/3 tan^(-1) (x/3)]_0^3` `= [(1/3 tan^(-1) 1) – 0]` `= 1/3 xx pi/4` `= pi/12`