freeCodeCamp/guide/english/mathematics/area-between-a-curve-and-the-x-axis/index.md

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title: Area-between-a-curve-and-X-axis
---

## Area Between a Curve and the X Axis


To find the area between a curve and the x-axis, the most preferred tool is [definite integration](https://www.mathsisfun.com/calculus/integration-definite.html) of the given curve.

To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b.

![img](https://upload.wikimedia.org/wikipedia/commons/f/f2/Integral_as_region_under_curve.svg)

![img](https://latex.codecogs.com/gif.latex?%5Clarge%20S%20%3D%20%5Cint_%7Ba%7D%5E%7Bb%7D%20f%28x%29%20dx)


## Some Examples





NOTE: Areas under the x-axis will come out negative and areas above the x-axis will be positive. This means that you have to be careful when finding an area which is partly above and partly below the x-axis.

#### More Information:
- [Interactive lessons for Area under the Curve](https://www.intmath.com/applications-integration/2-area-under-curve.php)