We discuss how to approximate the area under a curve.
Video Lecture
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This question is remarkably close to one of the first questions we posed this semester: how do you determine the exact value of , rather than getting an approximation using the “method of exhaustion” from the Ancient Greeks? The answer then, is the answer now - we need limits!
To see how we use limits, watch the above video for a nice visualization.
So, we’ve seen that by taking a limit of the number of rectangles to infinity, we can get a perfect approximation of the area under the given curve. The formula; is a bit intimidating, but it is so useful that, we will see, there is a different way to notate this, as well as a surprisingly quick way to calculate this sum!