length of an arc

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The length of the straight line segment obtained by straightening the arc without stretching it. Except where the curve forms part of a known shape, the arc length has to be calculated by integration, and the form depends on the coordinates used:

in Cartesian coordinates:

in polar coordinates: for the length between r=u and r=v or if the integration is carried out for a range of angles, it is in the form

in parameterized form (x(t), y (t) it will be

Subjects: Mathematics.

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