Refresh the students' memory about their basic algebraic skills by assigning them the task of creating and graphing functions that form various shapes and artwork. Give the students a specific list of the required functions including parabolas, ellipses, lines and vertexes and encourage them to create a picture using those types of functions. Examples of pictures that students could attempt might be a face, a musical instrument or a tree.
Once students learn how to integrate, have them put this into practice by doing some three-dimensional word problems. An example would be to have the student trace their foot onto a piece of graph paper and then determine the necessary formula to rotate it around either the "x" or "y" axis. Once they are done, have the students plug their equations into a graphing program and watch their feet rotate.
Newtonian physics offers the best projects for calculus due to its derivation and integration requirements. Consider, for example, having the students build a spring system to launch a car to a specific length. Because the students must take both the spring and frictional calculations into account, they will need to integrate their equations and determine the necessary spring forces.