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Numerical Integration Calculator

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.

Features

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

Prerequisites

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

Usage

  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.

Function Format

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))"

Example

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

Results

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 %

Graphical Representation

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

License

This project is licensed under the MIT License

Contributing

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

Happy coding!

Contributers

Author✍️