Where is a Riemann Sum applicable in real life?
Riemann sums help you approximate the area under a curve. In math class, we typically see polynomial or exponential functions (which are pretty easy to integrate). In real life, however, we rarely see these pretty functions. For example, it’s virtually impossible to find a function that exactly represents the contours of a leaf on a tree outside. If you wanted to find the area of a side of the leaf, you certainly can’t rely on plain integration. Riemann sums can help you approximate the area. In terms of even versus uneven intervals, there’s really not a huge difference from a mathematical perspective. It really depends on what information you have about the underlying curve.
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