3 INTEGRAL CALCULUS AND MODELLING questions Essay Example

  • Category:
    Mathematics
  • Document type:
    Math Problem
  • Level:
    Undergraduate
  • Page:
    1
  • Words:
    219

For 3 INTEGRAL CALCULUS AND MODELLING questions

In this case a = 0 b =64 f(x) = 3 INTEGRAL CALCULUS AND MODELLING questions 1

3 INTEGRAL CALCULUS AND MODELLING questions 2 = 3 INTEGRAL CALCULUS AND MODELLING questions 3 = 3 INTEGRAL CALCULUS AND MODELLING questions 4

3 INTEGRAL CALCULUS AND MODELLING questions 5 for each case of i

3 INTEGRAL CALCULUS AND MODELLING questions 6 = for each i

3 INTEGRAL CALCULUS AND MODELLING questions 7

Through expansion this equation is reduced to

3 INTEGRAL CALCULUS AND MODELLING questions 8-10) = 64

This gives n = 2.4

b) summation notations

Expression for upper Riemann sum

3 INTEGRAL CALCULUS AND MODELLING questions 9

Expression for lower Riemann sum

3 INTEGRAL CALCULUS AND MODELLING questions 10

c) Finding exact value of integral

3 INTEGRAL CALCULUS AND MODELLING questions 11 =3 INTEGRAL CALCULUS AND MODELLING questions 12 = 191.7

2 Evaluation of integrals

3 INTEGRAL CALCULUS AND MODELLING questions 13

3 INTEGRAL CALCULUS AND MODELLING questions 14

3 INTEGRAL CALCULUS AND MODELLING questions 15

(B-A)x (-5A-B) = 3 INTEGRAL CALCULUS AND MODELLING questions 16

Thus B-A = 1 and -5A –B = -2

Solving for A and B

A = 3 INTEGRAL CALCULUS AND MODELLING questions 17 B =1 3 INTEGRAL CALCULUS AND MODELLING questions 18

3 INTEGRAL CALCULUS AND MODELLING questions 19 = 3 INTEGRAL CALCULUS AND MODELLING questions 20

3 INTEGRAL CALCULUS AND MODELLING questions 21In3 INTEGRAL CALCULUS AND MODELLING questions 22

3 INTEGRAL CALCULUS AND MODELLING questions 23 = ( 3 INTEGRAL CALCULUS AND MODELLING questions 24In3 INTEGRAL CALCULUS AND MODELLING questions 25 — (3 INTEGRAL CALCULUS AND MODELLING questions 26In3 INTEGRAL CALCULUS AND MODELLING questions 27

b) 3 INTEGRAL CALCULUS AND MODELLING questions 28= 3 INTEGRAL CALCULUS AND MODELLING questions 29dx = 3 INTEGRAL CALCULUS AND MODELLING questions 30dx

3 INTEGRAL CALCULUS AND MODELLING questions 31dx

Using u = cosx du = -sinxdx

3 INTEGRAL CALCULUS AND MODELLING questions 32dx 3 INTEGRAL CALCULUS AND MODELLING questions 33

= 3 INTEGRAL CALCULUS AND MODELLING questions 34+C

= 3 INTEGRAL CALCULUS AND MODELLING questions 353 INTEGRAL CALCULUS AND MODELLING questions 363 INTEGRAL CALCULUS AND MODELLING questions 37

3 INTEGRAL CALCULUS AND MODELLING questions 38 = 3 INTEGRAL CALCULUS AND MODELLING questions 393 INTEGRAL CALCULUS AND MODELLING questions 40

c) 3 INTEGRAL CALCULUS AND MODELLING questions 41dx = 3 INTEGRAL CALCULUS AND MODELLING questions 42dx = In 3 INTEGRAL CALCULUS AND MODELLING questions 43

3 INTEGRAL CALCULUS AND MODELLING questions 44

Areas calculation

Curve 3 INTEGRAL CALCULUS AND MODELLING questions 45 Can be written as 3 INTEGRAL CALCULUS AND MODELLING questions 46

While curve 3 INTEGRAL CALCULUS AND MODELLING questions 47 can also be written as 3 INTEGRAL CALCULUS AND MODELLING questions 48

The required region given by

Areas bound by the y-axis and the line y =5 between coordinates 5, 25 and 5,625

3 INTEGRAL CALCULUS AND MODELLING questions 49 =3 INTEGRAL CALCULUS AND MODELLING questions 50 (5×625) – (5×25) =3125 – 125 =3000

Areas bound by the y-axis and the curve 3 INTEGRAL CALCULUS AND MODELLING questions 51between coordinates 4, 16 and 5,25

A2 = 3 INTEGRAL CALCULUS AND MODELLING questions 52 = 3 INTEGRAL CALCULUS AND MODELLING questions 53 = 83.33- 42.66 = 40.67

A3 = 3 INTEGRAL CALCULUS AND MODELLING questions 54 =3 INTEGRAL CALCULUS AND MODELLING questions 55 = 2500 — 44.7 = 2455.3

Required area = 3 INTEGRAL CALCULUS AND MODELLING questions 56+A2)-A3 = (3000 +40.67) -2455.3 = 585.37

Calculation volume

The volume is the space swept by the area about the axis x= -1

3 INTEGRAL CALCULUS AND MODELLING questions 57

=3 INTEGRAL CALCULUS AND MODELLING questions 58

= 11033 units