This Python script calculates numerical integration using various methods, such as the Trapezoidal Rule, Simpson's 1/3 Rule, Simpson's 3/8 Rule, and combinations of these rules.

• Numerical integration using different methods.
• Graphical representation of the function and integration area.

• Python 3.x
• Required Python libraries: matplotlib, pandas, numpy, math

1. Clone the repository to your local machine:

   git clone https://github.com/m-essam-s/Numerical_Integration.git
   cd Numerical_Integration

2. Run the script:

   python main.py

3. Enter the function, lower bound, and upper bound as prompted.

4. View the results and graphical representation.

The input function should be in the format of a valid Python expression. For example:

"0.2 + (25 * x) - (200 * (x**2)) + (675 * (x**3)) - (900 * (x**4)) + (400 * (x**5))"

if __name__=='__main__':
    Function = input("F(X) = ")
    LowerBound = eval(input("Lower bound = "))
    UpperBound = eval(input("Upper bound = "))
    
    Calc = Numerical_Integration(Function, LowerBound, UpperBound)
    print(Calc)
    Calc.Graph()

$ python main.py
F(X) =  (0.2+(25*x)-(200*(x**2))+(675*(x**3))-(900*(x**4))+(400*(x**5)))
Lower bound = 0.2
Upper bound = 0.8

The results will be displayed in tabular format, including the true value and percentage error for each integration method.

                               Result               |εₜ|
True Value                  |  1.2825416666851581                   0 %
Trapezoidal Rule            |  0.9127499999999996  28.832721485058464 %
Simpson's 1/3 Rule          |  0.7948000000000065   43.91758396977672 %
Simpson's 3/8 Rule          |  0.9564000000000059   32.51481795255984 %
Compination 1/3 & 3/8 Rule  |   1.267564117333339  10.558557909825753 %
1/3 & 3/8 & 1/3 & 3/8 Rule  |  1.4910980853333393   5.214372374852828 %

A plot of the function and the shaded area representing the integration will be displayed using matplotlib.

This project is licensed under the MIT License

If you find any issues or have suggestions for improvement, please feel free to open an issue or submit a pull request.

Happy coding!

• Mohamed Essam.

• FerventFrost.

• Mohamed Essam <m-essam-s>