Basic Engineering Mathematics, Fifth Edition

328 Basic Engineering Mathematics From 3 of Table 35.1, ∫ 5sin2θdθ=( 5 ) ( − 1 2 ) cos2θ+c =− 5 2 cos 2θ+c Problem 13. Determine ...

Introduction to integration 329 For example, the increase in the value of the integral x^2 asxincreases from 1 to 3 is written a ...

330 Basic Engineering Mathematics = { − 3 2 (− 1 ) } − { − 3 2 ( 1 ) } = 3 2 + 3 2 = 3 Problem 23. Evaluate ∫ 2 1 4cos3tdt ∫ 2 1 ...

Introduction to integration 331 The shaded area in Figure 35.1 is given by shaded area= ∫b a ydx= ∫b a f(x)dx Thus, determining ...

332 Basic Engineering Mathematics 40 30 20 10 5 0 1234 v (m/s) t(s) v  2 t^2  5 Figure 35.4 Problem 28. Sketch the graph y=x^3 ...

Introduction to integration 333 x 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 y 4 7 10.75 16 22.75 31 40.75 52 01234 x 4 50 40 30 20 10 y y 5 ...

334 Basic Engineering Mathematics Shaded area= ∫π/ 3 0 ydx = ∫π/ 3 0 sin2xdx= [ − 1 2 cos2x ]π/ 3 0 = { − 1 2 cos 2 π 3 } − { − ...

Revision Test 14 : Differentiation and integration This assignment covers the material contained in Chapters 34 and 35.The marks ...

List of formulae Laws of indices: am×an=am+n am an =am−n (am)n=amn am/n=n √ am a−n= 1 an a^0 = 1 Quadratic formula: Ifax^2 +bx+c ...

List of formulae 337 (v)Circle Area=πr^2 Circumference= 2 πr r r s  Radian measure: 2πradians=360degrees For a sector of circle ...

338 Basic Engineering Mathematics Areas of irregular figures by approximate methods: Trapezoidal rule Area≈ ( width of interval ...

List of formulae 339 Grouped data: mean,x ̄= ∑ fx ∑ f standard deviation,σ= √√ √ √ [∑{ f(x− ̄x)^2 } ∑ f ] Standard derivatives y ...

Answers Answers to practice exercises Chapter 1 Exercise 1 (page 2) 1.19kg 2. 16m 3. 479mm 4.− 66 5. £565 6. − 225 7.− 2136 8. − ...

Answerstopracticeexercises 341 Chapter 3 Exercise 8 (page 17) 1. 13 20 2. 9 250 3. 7 40 4. 6 125 5.(a) 13 20 (b) 21 25 (c) 1 80 ...

342 Basic Engineering Mathematics Chapter 5 Exercise 21 (page 34) 0 .32% 2. 173 .4% 3. 5 .7% 4. 37 .4% 128 .5% 6. 0. 20 7. 0. 0 ...

Answerstopracticeexercises 343 Chapter 8 Exercise 32 (page 55) 1.cubic metres, m^3 2. farad 3.square metres, m^2 4. metres per s ...

344 Basic Engineering Mathematics Chapter 10 Exercise 39 (page 69) 1.x^2 + 5 x+ 6 2. 2 x^2 + 9 x+ 4 4 x^2 + 12 x+ 9 4. 2 j^2 + ...

Answerstopracticeexercises 345 9.T= I PR L= XL 2 πf R= E I x=a(y− 3 ) C= 5 9 (F− 32 ) 14. f= 1 2 πCXC Exercise 47 (page 87 ...

346 Basic Engineering Mathematics 5.x= 2 ,y= 4 ,z= 5 6. x= 1 ,y= 6 ,z= 7 7.x= 5 ,y= 4 ,z= 2 8. x=− 4 ,y= 3 ,z= 2 9.x= 1. 5 ,y= 2 ...

Answerstopracticeexercises 347 Chapter 16 Exercise 62 (page 118) (a) 0.1653 (b) 0.4584 (c) 22030 (a) 5.0988 (b) 0.064037 (c) 40 ...