The Chemistry Maths Book, Second Edition

630 AppendixStandard integrals Reduction formulas Z Z sin cos sin cos sin mn mn m xxdx xx mn n mn = − +− 11 1 xxxdx ...

Solutions to exercises Chapter 1 Section 1.2 1.− 1 2. 7 3. 1 12 5.− 12 6.− 2 2 8. 328 9. 1228 10.− 11218 11. 126 12.− 1254 53 ...

632 Solutions to exercises (i) 67 (ii)− 3 (iii)− 31 (iv)− 197227 (i) 2 a 2 1 + 14 a 1 + 13 (ii) 2 y 4 1 + 14 y 2 1 + 13 (i) ...

Solutions to exercises 633 Chapter 3 Section 3.2 1.c 1 = 113 , (i) 1 (ii) 1 (i)π 236 (ii) 29 π 260 (iii) 2 π 23 (iv) (v) 3 π ( ...

634 Solutions to exercises (i)ln 16 (ii)ln 1223 (iii)ln 132 (iv)ln 12 (i)ln 1 x 2 (ii)ln(2x 1 − 1 3) (iii) 0 (iv)x (v)x 2 ...

Solutions to exercises 635 Section 4.8 × 1 sin 122 1 x 1 cos 3 (x 2 1 + 1 1) 1 tan 123 12 x 73.6.1 1 × 110 − 4 s ...

636 Solutions to exercises 47.neither: even: ; odd: Section 5.4 48.πab 49. 61254 Section 5.6 (i) 1 (ii) 66 (iii) 60 (i)l 3 23 ...

Solutions to exercises 637 Section 6.5 Section 6.6 68.tan − 1 ...

638 Solutions to exercises 11 − 13 x 1 + 13 x 2 1 − 1 x 3 11 + 112 x 1 + 154 x 2 1 + 1108 x 3 1 + 181 x 4 11 − 120 x 1 + 11 ...

Solutions to exercises 639 Section 7.8 Chapter 8 Section 8.2 61 − 12 i 2. 4 3. 6 i 4. 181 + 14 i 5.− 81 − 16 i 6. ...

640 Solutions to exercises (i) Section 8.7 125 50. 6265 Chapter 9 Section 9.1 (i) 0 (ii) 16 (iii) 36 (i) 1 (ii)− 322 (i ...

Solutions to exercises 641 Section 9.6 37.− 21 − 12 t 2 (1 1 − 1 t 2 ) 122 38.−(2 1 sin 1 t 1 + 1 3)e 2cost− 3 t 39.(−a 1 sin 1 ...

642 Solutions to exercises (i) (ii) 6 x 2 5 e − 2 x 1 − 11 Section 11.3 13.y 2 1 = 12 x 3 1 + 1 c 14. 16.y 3 1 = 13 ...

Solutions to exercises 643 Section 12.8 34.y 1 = 1 ae 2 x 1 + 1 (b 1 − 1 x)e −x 35.y 1 = 1 (a 1 + 1 bx 1 + 1 x 2 ...

644 Solutions to exercises Section 14.3 4.f(x,t) 1 = 1 Ae B(x− 2 t) 6.For separation constant λ 2 ; λ 2 1 = 1 0: f(x,y) 1 = ...

Solutions to exercises 645 Section 15.5 Section 15.6 Chapter 16 Section 16.2 (i)b 1 − 1 a,a 1 − 1 b (ii) (iii) (iv ...

646 Solutions to exercises 6 8.− 4 9. 30 (i)C 11 1 = 1 − 1 ,C 12 1 = 1 − 3 ,C 13 1 = 1 − 2 C 21 1 = 1 − 5 ,C 22 1 = 1 − 2 ,C 2 ...

Solutions to exercises 647 Section 18.3 16.not possible 18.(2 2 −1) 21.not possible 22. 25.not possible 26 ...

648 Solutions to exercises (i) (ii) (iii) Section 18.6 (i) (iii) and (vi) A − 1 1 = 1 A T 1 = 1 A Section 18.7 (i)E ...

Solutions to exercises 649 20.For (i)E 1 1 = 1 α 1 + 1 φβ,E 2 1 = 1 α 1 + 1 (φ 1 − 1 1)β, E 3 1 = 1 α 1 − 1 (φ 1 − 1 1)β,E 1 1 = ...