In more tangible, real-world applications, the trapezoidal rule is often used in civil engineering: ![]() While other equations such as Simpson’s Rule can provide an even more accurate integral – that is, the total area under the graph – the trapezoidal rule is still used for periodic functions and double exponential functions. The first known use of the trapezoidal rule dates to 50 BCE when it was used for integrating Jupiter’s velocity on the ecliptic. And, while you can solve this by hand, there’s no need to because of the free trapezoidal rule calculators and software available to do it for you. If you’re taking calculus or are an engineer, you likely use the trapezoidal rule on a regular basis. The more trapezoids you use, the more accurate the total area calculated will be. ![]() All the individual trapezoid areas are then added together to calculate the total area under the x-y points making up the curving line. ![]() The trapezoidal rule creates a series of side-by-side, left-to-right trapezoids under the curve. This is where the trapezoidal rule comes into play. While this is easy enough to do with a straight line, a curving, irregular line is more problematic. In addition to marking these specific data points, you may need to calculate the area of the region under the line. Imagine you have an x-y graph with a plotted line running from left to right.
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