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3 INTEGRAL CALCULUS AND MODELLING questions Essay Example
- Category:Mathematics
- Document type:Math Problem
- Level:Undergraduate
- 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