Convert Degrees To Radians: Simple Guide With Examples

Arc length

s = rθ(radius x central angle *in radians*)

Arc length is defined as the distance along a part of a curve or the length of the curve. It is denoted by the symbol s and is usually measured in units of length (such as meters, centimeters, or feet).

The formula to find the arc length of a curve is:

s = ∫√(1 + [f'(x)]^2) dx, where f'(x) is the derivative of the function.

To find the arc length, you need to integrate the square root of the sum of the squares of the function’s derivative over the interval in question. This formula computes the arc length of any curve defined by f(x) with its endpoints being a and b.

For example, consider the curve y = x^2 from x = 0 to x = 1. To find the arc length of this curve on this interval, we can use the formula:

s = ∫0^1 √(1 + [2x]^2) dx

simplifying the expression further,

s = ∫0^1 √(1 + 4x^2) dx

We can then evaluate the integral using various techniques such as substitution or integration by parts. Once we have found the value of the integral, we obtain the arc length of the curve between the given endpoints.

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