From the course: Complete Guide to Calculus Foundations for Data Science
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Arc length
From the course: Complete Guide to Calculus Foundations for Data Science
Arc length
- [Instructor] Let's dive into another integral application. You are able to discover how to find the area beneath the curve or between two curves, but what about determining the length of the curve itself? This is what you'll explore in this video. When you want to find the length of a curve between two points, this is what you call arc length. You can think of arc length as the path you would take along the function itself. This can be incredibly useful to use when finding the distance of projectiles over non-linear distances. When calculating arc length, there are two main formulas you can use depending on if it is a function of x or y. If you have a function f(x) over a closed bounded interval, a to b, the arc length is given by the integral of a to b of the square root of one plus the derivative of f(x) squared dx. If you have a function g(y) over closed bounded intervals, c to d, the arc length is given by the integral of c to d of the square root of one plus the derivative of…
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