# 3 INTEGRAL CALCULUS AND MODELLING questions Essay Example

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

For In this case a = 0 b =64 f(x) =  = =  for each case of i = for each i Through expansion this equation is reduced to -10) = 64

This gives n = 2.4

b) summation notations

Expression for upper Riemann sum Expression for lower Riemann sum c) Finding exact value of integral = = 191.7

2 Evaluation of integrals   (B-A)x (-5A-B) = Thus B-A = 1 and -5A –B = -2

Solving for A and B

A = B =1  =  In  = ( In — ( In b) = dx = dx dx

Using u = cosx du = -sinxdx dx = +C

=    =  c) dx = dx = In  Areas calculation

Curve Can be written as While curve can also be written as The required region given by

Areas bound by the y-axis and the line y =5 between coordinates 5, 25 and 5,625 = (5×625) – (5×25) =3125 – 125 =3000

Areas bound by the y-axis and the curve between coordinates 4, 16 and 5,25

A2 = = = 83.33- 42.66 = 40.67

A3 = = = 2500 — 44.7 = 2455.3

Required area = +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 = = 11033 units