Area under a curve
The area between a curve and the x-axis can be calculated with the definite integral.
Here is a short overview. You can find more information about calculating areas with integrals in the corresponding article.
Functions without change of sign
The area under a function $f(x)$ without change of sign over $[a; b]$ corresponds to the absolute value of the definite integral.
Functions with change of sign
The area is partly above and partly below the x-axis. The divided areas must therefore be calculated and added separately.
Area between curves
The enclosed area in the interval $[a; b]$ is calculated by the formula: