# 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 $y = {x^3} - x$ and the x-axis.

Since $y = 0$ at x-axis, so for the points of intersection of the curve $y = {x^3} - x$ at x-axis, put $y = 0$ this implies that ${x^3} - x = 0$

The curve cuts x-axis only at $x = - 1,\,\,\,x = 0,\,\,\,x = 1$ as shown by the graph of the given function $y = {x^3} - x$.

It is also clear above graph that $y \geqslant 0$ for $- 1 \leqslant x \leqslant 0$ and $y \leqslant 0$ for $0 \leqslant x \leqslant 1$, so the required area is split into two regions and is given by

Which shows that the area under the curve.