Which method is often used for numerical integration?

The trapezoidal rule is a commonly used method for numerical integration because it provides a way to estimate the definite integral of a function by approximating the area under the curve with trapezoids. This method works by dividing the integration interval into smaller segments, calculating the area of each trapezoid formed by connecting points on the curve with straight lines, and then summing these areas to achieve an approximation of the total area under the curve.

This approach is particularly effective because it balances the function values at the endpoints of each interval, leading to a simple yet effective means of capturing the behavior of the function being integrated. The trapezoidal rule has a relatively low computational cost and produces accurate results, especially when the function is reasonably smooth and continuous over the interval being considered. This is why it is favored for numerical integration tasks, making it a well-established technique in engineering and applied mathematics.