The Area Bounded by the Curve y=x^3-x and the x-axis
In this tutorial we shall find the area bounded by the curve and the x-axis.
Since at the x-axis, for the points of intersection of the curve
at x-axis, put
. This implies that
The curve cuts the x-axis only at , as shown by the graph of the given function
.

It is also clear from the graph above that for
and
for
, so the required area is split into two regions and is given by