Area Between a Curve and the x-Axis

Area Between a Curve and the x-Axis

If $$f(x)$$ changes sign at roots:

$$x_1,x_2,\ldots,x_n$$

then the total area is:

$$A=\sum_{i=0}^{n}\left|\int_{x_i}^{x_{i+1}}f(x)\,dx\right|$$

Usage

- Used to calculate total geometric area when the curve crosses the $$x$$-axis multiple times.