Arc length
In mathematics, curves have what is known as an "arc-length". This is the length the curve would have if it were straightened, such that, it became a line. The arc-length, of some curved function, f(x), between points a and b, is equal to the integral of the square root of the quantity, one plus the square derivatived (or squared slope) of f(x) multiplied by the derivative of x --
- s = ∫ √ (1 + [df/dx(x)]2dx.
The arc-length formula is derived from the distance formula.
For a more formal treatment, see rectifiable curve.
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