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Riemann rectangles are a visual and conceptual way to approximate the area under a curve by dividing the interval on the x-axis into smaller subintervals and drawing rectangles over each one. The height of each rectangle is determined by the value of the function at a specific point within that subinterval—this could be the left endpoint, right endpoint, or midpoint. As the number of rectangles increases (meaning the width of each one decreases), the total area of all the rectangles gets closer
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The rectangle rule is one of the simplest numerical methods for approximating the definite integral of a function. It works by dividing the interval into equal subintervals and approximating the area under the curve using rectangles whose heights are determined by the function value at a chosen point in each subinterval (left endpoint, right endpoint, or midpoint). While easy to implement and computationally fast, the rectangle rule can introduce significant error, especially when the function i
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