Cambridge Additional Mathematics

Applications of integration (Chapter 16) 441 Example 4 Self Tutor Use Zb a [yU¡yL]dx to find the area bounded by thex-axis and y ...

442 Applications of integration (Chapter 16) Example 6 Self Tutor Find the total area of the regions contained by y=f(x) and the ...

Applications of integration (Chapter 16) 443 8 Sketch the circle with equation x^2 +y^2 =9. a Explain why the upper half of the ...

444 Applications of integration (Chapter 16) DISTANCES FROM VELOCITY GRAPHS Suppose a car travels at a constant positive velocit ...

Applications of integration (Chapter 16) 445 Example 7 Self Tutor The velocity-time graph for a train journey is illustrated in ...

446 Applications of integration (Chapter 16) DISPLACEMENT AND VELOCITY FUNCTIONS In this section we are concerned withmotion in ...

Applications of integration (Chapter 16) 447 Example 8 Self Tutor A particle P moves in a straight line with velocity function v ...

448 Applications of integration (Chapter 16) 4 The velocity of a moving object is given by v(t)=32+4t ms¡^1. a If s=16m when t=0 ...

Applications of integration (Chapter 16) 449 ii The particle changes direction when t=5s. Now s(5) =¡^13 (5)^3 + 2(5)^2 + 5(5) = ...

16 APPLICATIONS OF INTEGRATION 3 Does Z 3 ¡ 1 f(x)dx represent the area of the shaded region? Explain your answer briefly. 4 Det ...

Applications of integration (Chapter 16) 451 5 OABC is a rectangle and the two shaded regions are equal in area. Findk. 6 The sh ...

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Answers 453 EXERCISE 1A 1a 52 D b 62 =G cd=2fa,e,i,o,ug df 2 , 5 gμf 1 , 2 , 3 , 4 , 5 , 6 g ef 3 , 8 , 6 g*f 1 , 2 , 3 , 4 , 5 ...

454 Answers biThere are two points of intersection between the straight line and the circle. iiThere is one point of intersectio ...

Answers 455 6afb,d,e,hg bfe,f,h,i,jg c fa,c,f,g,i,j,kg dfa,b,c,d,g,kg efe,hg ffb,d,e,f,h,i,jg gfa,c,g,kg h fa,b,c,d,f,g,i,j,kg 7 ...

456 Answers cd ef gh ij kl EXERCISE 1G 1a 7 b 14 c 14 d 7 e 5 f 9 2ab+c b c+d c b da+b+c e a+c+d f d 3a i 2 a+4 ii 4 a+4 iii 3 a ...

Answers 457 8a if 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24 g ii f 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30 g iii f 1 , 2 , 3 , 6 g iv f 1 , 2 , 3 ...

458 Answers hDomain=fx:x 2 Rg, Range=fy:y>¡ 2 g i Domain=fx:x 6 =§ 2 g, Range=fy:y 6 ¡ 1 ory> 0 g 2af(x)defined forx>¡ ...

Answers 459 gx=1or^13 hx=0or 3 i x=¡ 2 or^145 2ax=¡^14 or^32 bx=¡ 6 or¡^43 c x=^12 dx=^52 ex=0or^25 f x=¡ 2 or 0 EXERCISE 2D.3 1 ...

460 Answers ef gh ij kl 4a b c EXERCISE 2G 1a Domain off(x)is fx:¡ 26 x 60 g Range off(x)is fy:0 6 y 65 g Domain of f¡^1 (x)is f ...