There is something satisfying about coloring. It's straightforward and fun.
This activity asks students to do some coloring. Here's how it works: Students are provided with a series of definite integrals. Each integral represents an area. The students are asked to color in this area on the grid provided.
There are two versions: One with the graphs provided and one without the graphs.
This activity is appropriate for both AP Calculus AB and BC.
An answer key is included.
Put on some nice and relaxing music. Start with a moment of quietness to get everyone in the right mindset. Then, "Today we are going to de-stress by coloring. I want you to develop some intuition regarding integrals and area. You don't have to worry about graphing(*) or integrating anything--just color!"
When might you use this? I recommend using it as an introduction to a lesson on finding the area between two curves. You can give it to students before introducing the concept formally and let them figure out the connections.
Another option is to give it to students as a review, perhaps in preparation for a unit test.
One more thing: If you want, after the students have finished coloring, you can have them cut out each integral and graph separately and either make flashcards with them (integral on the front, graph on the back) or use them as a "matching" activity.
If you like this, then please check out my complete lesson on Areas Between Curves:
Areas Between Curves
*Unless, of course, you give your students the version without the graphs. :)