Numerical Integration for Arc Length

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I'm seeking to calculate arc length without referring to functions that make use of angle measures or pi. This description of numerical integration seems like a good way to go, but I am not calculating correctly. I'm pretty sure that I understand what dx indicates and from the context I have solved for the x in the denominator under the radical using the given solution to gain insight, but I am failing to recognize which value x should be when it comes time to work the example with other coordinate values. I suspect I am overlooking something terribly obvious; apologies and thanks.