Arclength
To find the arclength of a curve , chop it up into infinitely small pieces of length
as follows:
To find the arclength of a curve , chop it up into infinitely small pieces of length
as follows:
Then add up all the lengths of the pieces to get the length of the whole curve: .
When you evaluate this integral, you get the arclength .
It is clear from the diagrams that the polar coordinate version is way harder than the cartesian coordinate version, so just work in terms of and convert to
at the end.
To get the length of the section of curve between and
, just add up the pieces between
and
:
To get the length of the section of curve between and
, just add up the pieces between
and
: