Archimedes showed that the area of a parabolic arch is equal to 2/3 the product of its base and height.
a) graph the part of the parabola bounded by y=9-x^2 and the x-axis (referred to as an arch). Use an appropriate integral to find this area.
b) find the base and height of the arch and verify Archimedes' formula.
c) prove Archimedes' formula for a general parabola.