## Finding the Length of a Curve

The applet below computes the length of a broken-line
approximation to a given curve. This curve is the
graph of a polynomial of degree three or less. The
coefficients are listed in the boxes just above
the graph. In the start-up exampel they are
0, 1, 0, 0, correspoding to the graph
y = x^{2},

a parabola.
Graph

#### Notes

Use the button "+" to increase the number of segments
in the broken-line approximation, hence to increase its
accuracy. As the number of segments increases, the'
length of the broken-line curve gets closer and closer
to the arc length of the curve. Thus the arc length
is limit value of these approximations:

lim( L_{n} ) = L

where L_{n} is the length of the n-segment
approximation and L is the length of the curve.
**Question:** What is the arc length of the given
parabola?

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Last modified by jac at 14:05 on 12/21/1997.