# Integrals

Use the Desmos Graphing 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 graph shown in the video (including taking a look at what's inside the "visual" folder), click here.

## Definite Integrals

Simply type int in an expression line to bring up an integration template. Additionally, you can access the integration template from the Functions menu on the keyboard, under Miscellaneous functions.

Type in your upper bound, lower bound, integrand, and differential ($$dx$$ in the example pictured above), and Desmos will evaluate your definite integral.

Use variables and sliders in the place of your upper and lower bound to show how the result changes as the bounds change.

## Indefinite Integrals and Infinite Limits of Integration

It's also possible to graph the output of some indefinite integrals by including x in the upper bound, 0 in the lower bound, and integrating with respect to a variable other than x.

Desmos will evaluate convergent integrals with infinite limits. Type infinity into either the upper or lower bound!

Divergent integrals with infinite limits will give a result of undefined in the expression list.

Use variables and sliders to build understanding of integrals with infinite limits.

## Integrals In Action

### Example Graph

Explore the Fundamental Theorem of Calculus.

### Example Graph

Explore arc length by integration.

### Example Graph

Explore different integration bounds using lists, variables, and sliders.