7A_2016-2017_H2_Maths_Integration_Techniques_Assignment_(Final)

National Junior College Mathematics Department 2016 Integration Techniques Page 1 of 1 National Junior College 2016 – 2017 H2 Mathematics Integration Techniques Equations and Inequalities Assignment Name: ____________________________________________ Class: 1ma2___ / 1IPma21____ / 1IPma22____ Subject Tutor: _________________ You are advised to complete this ungraded piece of assignment in on e sitting, and to use only MF26. This will allow you to diagnose the weak sub-topic(s) to focus on in your subsequent revision. 1 Find (a) ln(1 2 ) d,12 x xx     (b) 2sec ln cos dx x x . [5] 2 (a) By using the substitution ux 1 , find 2 1 d 4 x xx    . [4] (b) By using the substitution cos5x , find 225 dx xx    . [6] 3 (a) Write down the constants A and B such that, for all values of x,  2 5 1x A x B    . Hence find 2 25 d .25 x xxx     [5] (b) By considering the derivative of   2tan ,x find   3 2 2sec dx x x . [5] 4 (i) Show that   32 2 2 d1 .d 1 1 x x x x     [1] (ii) By using the substitution 1 ,x y find 2 1 d 1 x xx    . [3] (iii) Find   3 2 21 ln dx x x x   . [3] Suggested Duration: 55min Time