What is numerical integration used for in engineering computation?

Numerical integration is an essential technique in engineering computation used to approximate the integral of a function. Since many functions encountered in engineering problems do not have analytical solutions or are difficult to integrate using traditional methods, numerical techniques provide a means to obtain a value for the integral using approximation methods such as the trapezoidal rule, Simpson’s rule, or other numerical algorithms.

This approach is particularly useful in scenarios where the function may be complex, defined only at discrete points, or when an exact solution is not necessary. Engineers frequently rely on numerical integration for applications such as calculating areas under curves, determining the center of mass, or evaluating physical quantities like work or energy that can be represented mathematically through integrals.

The other options do not pertain to the primary purpose of numerical integration. For instance, calculating averages involves different statistical techniques, while deriving functions directly relates to differentiation. Additionally, data trend analysis usually involves graphical representation or statistical methods rather than integration. Thus, the focus of numerical integration specifically on approximation techniques for finding integrals makes it the correct choice in this context.