积分演示.frm

Visual Basic课程举例1 有很好的例题

VERSION 5.00
Begin VB.Form Form1 
   Caption         =   "数值积分"
   ClientHeight    =   3915
   ClientLeft      =   60
   ClientTop       =   345
   ClientWidth     =   8670
   LinkTopic       =   "Form1"
   ScaleHeight     =   3915
   ScaleWidth      =   8670
   StartUpPosition =   3  '窗口缺省
   Begin VB.CommandButton Command2 
      Caption         =   "四维“球”"
      Height          =   495
      Left            =   1560
      TabIndex        =   10
      Top             =   3240
      Width           =   1215
   End
   Begin VB.CommandButton Command1 
      Caption         =   "二元函数积分"
      Height          =   495
      Left            =   120
      TabIndex        =   9
      Top             =   3240
      Width           =   1455
   End
   Begin VB.TextBox Text3 
      Height          =   375
      Left            =   120
      TabIndex        =   4
      Top             =   2580
      Width           =   2655
   End
   Begin VB.TextBox Text2 
      Height          =   375
      Left            =   1440
      TabIndex        =   3
      Top             =   1560
      Width           =   1335
   End
   Begin VB.TextBox Text1 
      Height          =   375
      Left            =   120
      TabIndex        =   2
      Top             =   1560
      Width           =   1095
   End
   Begin VB.ComboBox Cbofunc 
      Height          =   300
      Left            =   120
      TabIndex        =   1
      Text            =   "select"
      Top             =   600
      Width           =   2655
   End
   Begin VB.PictureBox PicFunc 
      BackColor       =   &H00FFFF80&
      Height          =   3555
      Left            =   3000
      ScaleHeight     =   3495
      ScaleWidth      =   5475
      TabIndex        =   0
      Top             =   120
      Width           =   5535
   End
   Begin VB.Label Label4 
      Caption         =   "被积函数"
      Height          =   255
      Left            =   120
      TabIndex        =   8
      Top             =   240
      Width           =   2655
   End
   Begin VB.Label Label3 
      Caption         =   "积分值"
      Height          =   255
      Left            =   120
      TabIndex        =   7
      Top             =   2160
      Width           =   2535
   End
   Begin VB.Label Label2 
      Caption         =   "终值"
      Height          =   255
      Left            =   1440
      TabIndex        =   6
      Top             =   1200
      Width           =   975
   End
   Begin VB.Label Label1 
      Caption         =   "初值"
      Height          =   255
      Left            =   240
      TabIndex        =   5
      Top             =   1200
      Width           =   975
   End
End
Attribute VB_Name = "Form1"
Attribute VB_GlobalNameSpace = False
Attribute VB_Creatable = False
Attribute VB_PredeclaredId = True
Attribute VB_Exposed = False
'积分演示程序。改编：曹新国，2004-3-14
'最后修改于 2006-4-5 晚。
DefDbl X-Z
Const PI = 3.14159265358979
Dim x0(10)
Dim x1(10)


Private Sub Cbofunc_Click()
   Dim xx0, xx1, h, s, t, x, n%, i%
    xx0 = x0(Cbofunc.ListIndex)         '获得被积函数的初值
    xx1 = x1(Cbofunc.ListIndex)
    Text1.Text = xx0
    Text2.Text = xx1
    PicFunc.Cls
    PicFunc.Scale (-0.5, 1.5)-(4, -1.2) '定义图形框系坐标
    PicFunc.Line (-0.5, 0)-(4, 0)      '画X轴
    PicFunc.Line (0, 1.5)-(0, -1.2)    '画Y轴
    PicFunc.Line (xx0, 1)-(xx1, 1)     'y=1
    PicFunc.Line (xx0, -1)-(xx1, -1)   'y=-1
    PicFunc.Line (xx0, 0)-(xx0, 0.1)   '画积分初值刻度和初值
    PicFunc.CurrentX = xx0
    PicFunc.CurrentY = -0.02
    PicFunc.Print xx0
    PicFunc.Line (xx1, -1)-(xx1, 1)   '画积分终值刻度和终值
    PicFunc.CurrentX = xx1
    PicFunc.CurrentY = -0.02
PicFunc.Print xx1
    n = 300                          '积分面积为40等份
    h = (xx1 - xx0) / n
    s = 0
    x = xx0
    For i = 1 To n
       Select Case Cbofunc.Text
            Case "Sin"
                t = (Sin(x) + Sin(x + h)) / 2
            Case "Cos"
                t = (Cos(x) + Cos(x + h)) / 2
            Case "0.3*(x^2-x+1)"
                t = 0.3 * (x ^ 2 - x + 1)
            End Select
        PicFunc.Line (x, 0)-(x, t)       '画出该函数值
            s = s + t * h                '累加面积
        x = xx0 + (xx1 - xx0) / n * i
    Next i
    Text3.Text = s
End Sub

Private Sub Command1_Click()
V = 0
dx = 1 / 200
dy = 1 / 200
For x = -1 To 1 Step 1 / 200
For y = -1 To 1 Step 1 / 200
   z = 1 - (x ^ 2 + y ^ 2)
   If z > 0 Then
      vi = dx * dy * Sqr(z) * 2
      V = V + vi
   End If
Next y
Next x
MsgBox "单位球(r=1)体积V=" & V & vbCrLf & "精确值V=" & 4 * PI / 3
End Sub

Private Sub Command2_Click()
'广义积分学的n重积分知识，就能轻而易举地算出一个100维空间里的“正方体”（n维单纯形）的“体积”

'V(n）＝a^n/n!(a边长，即体积等于a的n次方再除以n的阶乘）

'其中a≥X1+X2+……+Xn，Xi≥0

'另外，一个n维球的体积V（n）的计算公式是


'V（2m）＝〔π^m)R^2m〕/（2m）！     …… （n＝2m）              〈1〉

'V(2m＋1）＝[2（2π）^m][R^(2m+1)]/（2m+1)!!   ……（n＝2m＋1）    〈2〉
'
'学了微积分，任何一个人都算出四维球的体积1/2*Pi^2*R^4，表面积2*PI^2*R^3，由此还可以推广到5维，6维直至n维，你能不能归纳出来呢？
V = 0
dx = 1 / 50
dy = 1 / 50
dz = 1 / 50
For x = -1 To 1 Step 1 / 50
For y = -1 To 1 Step 1 / 50
For z = -1 To 1 Step 1 / 50
   U = 1 - (x ^ 2 + y ^ 2 + z ^ 2)
   If U > 0 Then
      vi = dx * dy * dz * Sqr(U) * 2
      V = V + vi
   End If
Next z
Next y
Next x
MsgBox "四维单位球（r=1）的" & vbCrLf & "球体积V=" & V & vbCrLf & "精确值V=" & 1 ^ 4 * PI ^ 2 / 2

End Sub

Private Sub Form_Load()
  Font.Size = 20
    Cbofunc.AddItem "Sin"
    Cbofunc.AddItem "Cos"
    Cbofunc.AddItem "0.3*(x^2-x+1)"
    x0(0) = 0: x1(0) = PI
    x0(1) = 0: x1(1) = PI
    x0(2) = 0: x1(2) = 2.2

End Sub