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The area under the curve
from
to
is 54.
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Did you know that the method of Riemann sums, which you’re using here to find the area under a curve, dates back to the early 19th century? Developed by mathematicians like Bernhard Riemann, this technique laid the groundwork for integral calculus as we know it today. It helps bridge the gap between discrete sums and continuous functions, making it a foundational concept in understanding calculus!
In real-world applications, Riemann sums are used in various fields, such as physics for calculating distances, in economics for finding consumer surplus, and in engineering to assess loads on structures. By evaluating areas under curves, engineers can predict material stress or optimize designs. So, the next time you’re crunching numbers for a project, remember you’re tapping into a powerful mathematical tool that touches many aspects of our lives!