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Task/Numerical-integration/FreeBASIC/numerical-integration.basic

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+' version 17-09-2015
+' compile with: fbc -s console
+
+#Define screen_width 1024
+#Define screen_height 256
+ScreenRes screen_width, screen_height, 8
+Width screen_width\8, screen_height\16
+
+Function f1(x As Double) As Double
+    Return x^3
+End Function
+
+Function f2(x As Double) As Double
+    Return 1/x
+End Function
+
+Function f3(x As Double) As Double
+    Return x
+End Function
+
+Function leftrect(a As Double, b As Double, n As Double, _
+ByVal f As Function (ByVal As Double) As Double) As Double
+
+    Dim As Double sum, x = a, h = (b - a) / n
+
+    For i As UInteger = 1 To n
+        sum = sum + h * f(x)
+        x = x + h
+    Next
+
+    leftrect = sum
+End Function
+
+Function rightrect(a As Double, b As Double, n As Double, _
+ByVal f As Function (ByVal As Double) As Double) As Double
+
+    Dim As Double sum, x = a, h = (b - a) / n
+
+    For i As UInteger = 1 To n
+        x = x + h
+        sum = sum + h * f(x)
+    Next
+
+    rightrect = sum
+End Function
+
+Function midrect(a As Double, b As Double, n As Double, _
+ByVal f As Function (ByVal As Double) As Double) As Double
+
+    Dim As Double sum, h = (b - a) / n, x = a + h / 2
+
+    For i As UInteger = 1 To n
+        sum = sum + h * f(x)
+        x = x + h
+    Next
+
+    midrect = sum
+End Function
+
+Function trap(a As Double, b As Double, n As Double, _
+ByVal f As Function (ByVal As Double) As Double) As Double
+
+    Dim As Double x = a, h = (b - a) / n
+    Dim As Double sum = h * (f(a) + f(b)) / 2
+
+    For i As UInteger = 1 To n -1
+        x = x + h
+        sum = sum + h * f(x)
+    Next
+
+    trap = sum
+End Function
+
+Function simpson(a As Double, b As Double, n As Double, _
+ByVal f As Function (ByVal As Double) As Double) As Double
+
+    Dim As UInteger i
+    Dim As Double sum1, sum2
+    Dim As Double h = (b - a) / n
+
+    For i = 0 To n -1
+        sum1 = sum1 + f(a + h * i + h / 2)
+    Next i
+
+    For i = 1 To n -1
+        sum2 = sum2 + f(a + h * i)
+    Next i
+
+    simpson = h / 6 * (f(a) + f(b) + 4 * sum1 + 2 * sum2)
+End Function
+
+' ------=< main >=------
+
+Dim As Double y
+Dim As String frmt = " ##.##########"
+
+Print
+Print "function     range       steps  leftrect      midrect       " + _
+                              "rightrect     trap          simpson "
+
+Print "f(x) = x^3   0 - 1         100";
+Print Using frmt; leftrect(0, 1, 100, @f1); midrect(0, 1, 100, @f1); _
+rightrect(0, 1, 100, @f1); trap(0, 1, 100, @f1); simpson(0, 1, 100, @f1)
+
+Print "f(x) = 1/x   1 - 100      1000";
+Print Using frmt; leftrect(1, 100, 1000, @f2); midrect(1, 100, 1000, @f2); _
+                    rightrect(1, 100, 1000, @f2); trap(1, 100, 1000, @f2); _
+                    simpson(1, 100, 1000, @f2)
+
+frmt = " #########.###"
+Print "f(x) = x     0 - 5000  5000000";
+Print Using frmt; leftrect(0, 5000, 5000000, @f3); midrect(0, 5000, 5000000, @f3); _
+                    rightrect(0, 5000, 5000000, @f3); trap(0, 5000, 5000000, @f3); _
+                    simpson(0, 5000, 5000000, @f3)
+
+Print "f(x) = x     0 - 6000  6000000";
+Print Using frmt; leftrect(0, 6000, 6000000, @f3); midrect(0, 6000, 6000000, @f3); _
+                    rightrect(0, 6000, 6000000, @f3); trap(0, 6000, 6000000, @f3); _
+                    simpson(0, 6000, 6000000, @f3)
+
+' empty keyboard buffer
+While InKey <> "" : Wend
+Print : Print "hit any key to end program"
+Sleep
+End