We can find an approximate value for the length of a curve between two
values
and
by approximating the curve by a series of line segments and adding up the length of each line segment. For the curve give above, the length of the line segment
so the length of the curve is approximately
if
and
We can write this as
and by letting
the sum becomes an integral:
Example: The curve below is
Find the length of the curve between
and
