In Apostol's book:
Archimedes made the surprising discovery that the area of the parabolic segment is exactly one-third that of the rectangle; that is to say, $A=b^3/3$, where $A$ denotes the area of the parabolic segment.
Why $A=b^3/3$? Shouldn't it be $A=b^2/3$? I thought that the area of a bidimensional space was given by the square ($x^2$) not with the cube($x^3$).
Notice I'm not so sure if I can call an area of bidimensional space.