Contour Integral Calculator
Explore complex analysis by calculating contour integrals. Input your function and contour to visualize and compute the integral value.
Input Parameters
Enter the complex function, contour parameterization, and the bounds for the parameter to calculate the contour integral.
Contour Integral Value
Contour Visualization
About Contour Integrals
In complex analysis, contour integrals are a powerful tool for evaluating integrals along paths in the complex plane. They are defined as integrals where the function to be integrated is evaluated along a curve in the complex plane. This calculator numerically approximates the contour integral for a given complex function f(z) and a contour parameterized by z(t) over a specified range of the parameter t. The visualization provides a graphical representation of the contour in the complex plane. Contour integrals have significant applications in physics, engineering, and various branches of mathematics, particularly in solving differential equations and analyzing complex systems.
- Function f(z): The complex function you wish to integrate. Express it in terms of 'z'.
- Contour z(t): Parameterization of the contour in terms of 't'. This defines the path of integration in the complex plane.
- Parameter Bounds: The range [a, b] for the parameter 't' that traces the contour.