TMJC Term 4 Revision Chapter 10 Techniques of Integration Questions

Term 4 Revision Topical Quick Check: Integration Techniques TMJC 2024 Page 1 of 2 JC1 H2 Mathematics (9758) Term 4 Revision Topical Quick Check Chapter 10 Integration Techniques 1 HCI Promo 9758/2022/Q8 (a) Find ( ) 13 tan 3 dt t t −  . [4] (b) Using the substitution 2 1ux=+ , show that ( ) 17 32 3 0 1dx x x + can be expressed as 41 331 d2 b a u u u− , where a and b are constants to be determined. Hence find the exact value of ( ) 17 32 3 0 1dx x x + . [5] 2 EJC Promo 9758/2022/Q6 (a) Find 231e d .xxx +  [1] (b) Find ( ) 2sin 5 d .xx [3] (c) Find 2 .41 d47 x xxx −+  [5] 3 MI PU2 P1 Promo 9758/2022/Q4 (i) Find cos 2 sin dx x x . [3] (ii) Find 1sin 2 2 e d 14 x x x − −   . [2] (iii) Find 2 5 d6 13 xxx++  . [3]

Term 4 Revision Topical Quick Check: Integration Techniques TMJC 2024 Page 2 of 2 Answer Key No. Year JC Answers 1 2022 HCI (a) ( ) ( ) 2 1 13 1 1tan 3 tan 32 2 6t t t t C−− − + + (b) 1209 56 2 2022 EJC (a) 2 131 e6 x c+ + (b) 11 sin102 20x x c−+ (c) ( ) 211 1 2 1ln 4 tan8 1 4 7 641 x cx x − −+ +  − + 3 2022 MI (i) 32 cos cos3 x x C− + + 11or cos3 cos62 x x c − + + (ii) 1sin 21 e2 x c − + (iii) 153tan22 x c− + +