## Finding the area under a curve

The applet below computes the area of a figure
made of rectangles which approximates the region
under the 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 rectangles
in the approximating figure, hence to increase its
accuracy. As the number of rectangles increases, the'
area of the figure gets closer and closer
to the area under the curve. Thus the area under the curve
is limit value of these approximations:

limit( A_{n} ) = A

where A_{n} is the are of the
approximating figure and A is the area of the given figure.
**Question:** What is the area under the
parabola?

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Last modified by jac at 14:06 on 12/21/1997.