The curve in polar coordinates
traced between
and
has arc length
Consider the curve
shown below.
The length of the curve is
#
Substitute
then
and the limits become
(the new lower limit) and
(the new upper limit).
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The curve in polar coordinatestraced betweenandhas arc lengthConsider the curveshown below.
The length of the curve is
#
Substitutethenand the limits become(the new lower limit) and(the new upper limit).