Our line integral calculator will help you compute the integral of a function along a specific curve with ease and precision.

## Line Integral Calculator

### How to Use the Line Integral Calculator

Follow these steps to calculate the line integral of a function:

- Enter your function for f(x, y) that you want to integrate along the path. Example format: 3*x + 2*y.
- Specify your parameterized path in terms of t for x(t) and y(t). Example format for a circle: x(t): cos(t), y(t): sin(t).
- Enter the start and end values for the parameter t to set the limits of the integral.
- Once all inputs are filled, click the “Calculate” button to obtain the result.

### How the Calculator Works

The calculator evaluates the line integral of a vector field along a given path by numerically integrating the function f(x, y) over the defined interval from t start to t end. It uses a numerical integration technique by discretizing the path into small elements and summing the contributions of each.

### Limitations

The precision of the result depends on the complexity of the function and the path chosen. The method is numerical, and therefore an increase in the number of steps will yield a more accurate result but will demand more processing time. If the inputted function or paths contain syntax errors or are not in terms of the variables used, the calculator will give an error message. This calculator is built to handle general cases, but should be used with care for functions or paths that exhibit discontinuities or singularities.