Use the Desmos Graphing Calculator, Geometry Tool, or 3D Calculator to investigate the beautiful world of integral calculus.

Get started with the video on the right, then dive deeper with the resources and challenges below.

If you'd like to explore the integral graph shown in the video (and open the "visual" folder), click here.

## Definite Integrals

Type *int* (or *integral* if working in the Geometry tool) in an expression line to bring up an integration template where you can type in a lower bound, upper bound, integrand, and differential (such as \(dx\)).

Let’s look at an example. If \(f(x)=\frac{1}{10}x^2+1\), and you take the integral from \(0\) to \(3\) of \(f(x)dx\), you’ll see this definite integral evaluates to \(3.9\). By clicking on the images, you can open the graphs and explore.

## Indefinite Integrals and Infinite Limits of Integration

It's also possible to graph the output of some indefinite integrals. One way to do so is by including \(x\) in the upper bound, \(0\) in the lower bound, and integrating with respect to a variable other than \(x\). Try graphing the integral from \(0\) to \(x\) of \(t^2 dt\).

Desmos will evaluate convergent integrals with infinite limits. Type *infinity* or *infty* into either the upper or lower bound! For example, if \(f(x)=\frac{1}{x^2}\), then the integral from \(1\) to infinity of \(f(x)dx\) is \(1\).

## Learn More

- Arc Length by Integration Example Graph
- Different Integration Bounds Example Graph
- Fundamental Theorem of Calculus Example Graph
- Functions
- Sliders and Movable Points

Please write in with any questions or feedback to support@desmos.com.