This macro in Excel computes the definite integral of a polynomial function of degree 5 using the Newton Raphson method. It initializes parameters like the coefficients, interval bounds, number of iterations. It then iteratively calculates the function value at each interval, sums the areas to get the integral. Finally it creates a chart to plot the function values.

1. Excel Macro for computing definite integral of a polynomial function of degree 5, using Newton Raphson method. - Upendra Lele/Nov 2014
Create a macro enabled Excel file with name “Integration of a function.xlsm”. Rename the first sheet as “Data” and type the details given in the image below. Add a command button on the sheet and rename it as compute.
Now click on Developer menu, click on Macros, delete all previous macros and add the following code in a new Macro:
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Public i, j, k, iterations, row_no, col_no As Integer Public a, b, coeff(10) As Double Public x, incr_x, fn, sum_area As Double Public chkval As Double
Sub Main() ' Solve a polynomial equation using Newton Raphson method ' Set up application progress message ' Application.Cursor = xlWait Application.DisplayStatusBar = True Application.StatusBar = "Calculations in progress. Please wait" Application.ScreenUpdating = False Application.DisplayAlerts = False Workbooks("Integration of a function.xlsm").Activate

2. Worksheets("Data").Activate ActiveSheet.ChartObjects(1).Select Selection.Delete
Range("B11:C2000").Delete Call init_params Call compute_integral If j >= iterations Then If sum_area = 0 Then Cells(8, 5) = "Not possible to calculate integral" End If End If
Call create_chart Workbooks(1).Activate Worksheets("Data").Activate Range("A1").Activate
End Sub
Sub init_params() ' Open files Workbooks(1).Activate Worksheets("Data").Activate a = Cells(6, 4).Value b = Cells(7, 4).Value Cells(8, 4) = "" Cells(8, 5) = "" row_no = 3 col_no = 3 coeff(0) = 0 k = 5
For i = 1 To 6 coeff(i) = Cells(row_no, col_no) col_no = col_no + 1 Next
iterations = 1000 x = a row_no = 11 Cells(row_no, 2).Value = x incr_x = (b - a) / iterations Call compute_fn sum_area = (fn * incr_x)

3. Cells(row_no, 3).Value = fn End Sub
Sub compute_integral() ' Generate successive approximations of X For i = 1 To iterations row_no = row_no + 1 x = (x + incr_x) Call compute_fn sum_area = sum_area + (fn * incr_x) Cells(row_no, 2).Value = x Cells(row_no, 3).Value = fn Next
Cells(8, 4) = sum_area Range("B11:B1011").NumberFormat = "0.000" Range("C11:C1011").NumberFormat = "0.00"
End Sub
Sub compute_fn() ' Compute the value of the function fn = ((coeff(1) * x ^ 5) + (coeff(2) * x ^ 4) + (coeff(3) * x ^ 3) + (coeff(4) * x ^ 2) + (coeff(5) * x) + coeff(6))
End Sub
Sub create_chart() Sheets("Data").Select Range("F20").Select ActiveSheet.Shapes.AddChart.Select With ActiveChart .ChartType = xlColumnClustered .SetSourceData Source:=Workbooks(1).Sheets("Data").Range("B10:C1011") .SeriesCollection(1).XValues = Range("B11:B1011") .SeriesCollection(1).Values = Range("C11:C1011") .Axes(xlCategory).TickLabels.Font.FontStyle = "Bold" .Axes(xlValue).TickLabels.Font.FontStyle = "Bold" .HasTitle = True .HasLegend = False .ChartTitle.Text = "Y = f(x)" .Parent.RoundedCorners = True .ChartArea.Height = 200 .ChartArea.Width = 300 .ChartArea.Format.Fill.ForeColor.RGB = RGB(204, 255, 255) .SetElement (msoElementChartTitleAboveChart)

4. .ChartTitle.Characters.Font.Size = 12 .SeriesCollection(1).Select End With
ActiveChart.SeriesCollection(2).Select Selection.Delete ' Resize and Position the chart on worksheet
With ActiveChart.Parent .Left = 230 .Width = 375 .Top = 110 .Height = 225 End With
Workbooks(1).Activate Worksheets("Data").Activate
End Sub