Weighted integrals are a mathematical concept used to calculate the area under a curve while giving different importance, or "weight," to different parts of the curve. This is useful in various applications, such as statistics and physics, where certain values need to be emphasized more than others. The weight is typically represented as a function that modifies the original function being integrated. In a weighted integral, the integral of a function f(x) is multiplied by a weight function w(x) . The formula can be expressed as \int w(x) f(x) \, dx . This approach allows for a more nuanced analysis of data, as it can highlight specific regions of interest, making it a valuable tool in fields like economics and engineering.