A Level Maths Notes: FP2 – The Length of a Curve
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
