' Mid-rectandle method
' for function f(x)= y(x) = x^2
Dim f(99)
a = 0
b = 1
n = 88
h = (b - a) / n
'
For k = 1 To n
x = a + k * (b - a) / n - h / 2
v = x ^ 2
f(k) = v
Next k
'
i = 0
For k = 1 To n
i = i + h * f(k)
Next k
MsgBox i
d1 = Abs(i - 1 / 3)
MsgBox d1
d2 = Abs(1 * 2 / (24 * n ^ 2))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd



-

' Rectandle method
' for function f(x)= y(x) = x
Dim f(99)
a = 0
b = 1
n = 88
h = (b - a) / n
'
For k = 0 To n
x = a + k * (b - a) / n
v = x
f(k) = v
Next k
'
i = 0
For k = 0 To n - 1
i = i + h * f(k)
Next k
MsgBox i
d1 = Abs(i - 1 / 2)
MsgBox d1
d2 = Abs(1 / (2 * n))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd




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' Trapezoidal rule
' for function f(x)= y(x) = x^2
Dim f(99)
a = 0
b = 1
n = 88
h = (b - a) / n
'
For k = 0 To n
x = a + k * (b - a) / n
v = x ^ 2
f(k) = v
Next k
'
i = 0
For k = 1 To n - 1
i = i + h * f(k)
Next k
i = i + (f(0) + f(n)) * h / 2
MsgBox i
d1 = Abs(i - 1 / 3)
MsgBox d1
d2 = Abs(2 / (12 * n ^ 2))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd




-


' Simpson's rule
' for function f(x)= y(x) = x
Dim f(99)
a = 0
b = 1
n = 8
h = (b - a) / n
'
For k = 0 To n
x = a + k * (b - a) / n
v = x
f(k) = v
Next k
'
i2j = 0
For j = 1 To n / 2 - 1
i2j = i2j + f(2 * j)
Next j
'
i2jm1 = 0
For j = 1 To n / 2
i2jm1 = i2jm1 + f(2 * j - 1)
Next j
'
i = (f(0) + 2 * i2j + 4 * i2jm1 + f(n)) * h / 3
'
MsgBox i
d1 = Abs(i - 0.5)
MsgBox d1
d2 = Abs(1 / (180 * n ^ 4))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd


-



' Rectangles formula
' for function f(x)= y(x) = x
a = 0
b = 1
n = 9
i = 0
h = (b - a) / n
For k = 1 To n
x = a + k * (b - a) / n
f = x
i = i + h * f
Next k
MsgBox i
d1 = Abs(i - 0.5)
MsgBox d1
d2 = Abs(1 / (2 * n))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd


-

' Simpson's rule
' for function f(x)= y(x) = x^4
Dim f(99)
a = 0
b = 1
n = 8
h = (b - a) / n
'
For k = 0 To n
x = a + k * (b - a) / n
v = x ^ 4
f(k) = v
Next k
'
i2j = 0
For j = 1 To n / 2 - 1
i2j = i2j + f(2 * j)
Next j
'
i2jm1 = 0
For j = 1 To n / 2
i2jm1 = i2jm1 + f(2 * j - 1)
Next j
'
i = (f(0) + 2 * i2j + 4 * i2jm1 + f(n)) * h / 3
'
MsgBox i
d1 = Abs(i - 1 / 5)
MsgBox d1
d2 = Abs(4 * 3 * 2 * 1 / (180 * n ^ 4))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd



-

Dim ff(3)
' for function f(x)= y(x) = x
a = 0
b = 1
n = 9
i = 0
h = (b - a) / n
ff(0) = 0
ff(1) = 0.5
ff(2) = 1
i = (b - a) / 6 * (ff(0) + 4 * ff(1) + ff(2))
MsgBox i
d1 = Abs(i - 0.5)
MsgBox d1
d2 = Abs(1 / (180 * n ^ 4))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd




-

' for function f(x)= y(x) = x
a = 0
b = 1
n = 9
i = 0
h = (b - a) / n
f0 = 0
fn = 1
For k = 1 To n - 1
f = k * (b - a) / n
i = i + h * f
Next k
i = i + (f0 + fn) * h / 2
MsgBox i
d1 = Abs(i - 0.5)
MsgBox d1
d2 = Abs(1 / (12 * n ^ 2))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd





-

' for function f(x)= y(x) = x^2
a = 0
b = 1
n = 100000
i = 0
h = (b - a) / n
For k = 1 To n
f = (k * (b - a) / n) ^ 2
i = i + h * f
Next k
MsgBox i
d1 = Abs(i - 1 / 3)
MsgBox d1
d2 = Abs(2 / (2 * n))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd


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' for function f(x)= y(x) = x^3
a = 0
b = 1
n = 100000
i = 0
h = (b - a) / n
For k = 1 To n
f = (k * (b - a) / n) ^ 3
i = i + h * f
Next k
MsgBox i
d1 = Abs(i - 1 / 4)
MsgBox d1
d2 = Abs(3 / (2 * n))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd

-

Dim ff(3)
' for function f(x)= y(x) = x^6
a = 0
b = 1
n = 2
i = 0
h = (b - a) / n
ff(0) = 0
ff(1) = 0.5 ^ 6
ff(2) = 1
i = (b - a) / 6 * (ff(0) + 4 * ff(1) + ff(2))
MsgBox i
d1 = Abs(i - 1 / 7)
MsgBox d1
d2 = Abs(6 * 5 * 4 * 3 / (180 * n ^ 4))
MsgBox d2
dd = Abs(d1 - d2)
MsgBox dd