Calc II - Integral Calculus - Projects - Part 1

After having taught Calc I and Calc III recently, now I find myself teaching Calc II, integral calculus, in the fall.  So again I am looking for projects.

These ideas are on Dave Martin's Real teaching means real learning blog.

• A project that combines creating images on GeoGebra with functions and then calculating the areas created.  I think students would like the GeoGebra part, but there is little motivation for the need of calculating the areas.  Another page talking about the same project with some nice pics.
• Can Kobe Bryant jump over a moving car?  A video shows him doing it.  Can we use calculus, including integration, to investigate this?
• Explain mathematically explaining everything you know about an irregularly shaped symmetrical object such as a bottle or a vase. Include detailed drawings and calculations.
• Create a video of an object in free-fall.  You must throw your object, and calculate the velocity of the object when it left your hand.  Appropriate measurements must be included.
• In "Calculus and the Justice System" students used mathematical models to argue both sides of a speeding ticket case.  The problem is reprised in this blog post.

Master Math Mentor - This site is for AP Calculus, but has some interesting projects or activities.  The downloads are free, but the page for opening them asks for an optional name and email address.

• The center of mass project asks students to calculate and then test the center of mass of a lamina, in this case a plexiglass sheet cut into a shape.  The students have to model the shape, calculate the center of mass, and then test it on a pencil set in a can of sand.  Requires the hardware to cut the plexiglass.  Think I could get a jigsaw with my departmental funds?
• The centroid worksheet is probably supposed to be done without integration, but I think some of the exercises would be good as introductory integral calculations.
• Differential equations modeling population growth is illustrated with a project using a deer population.
• The glass project has students model the shape of a glass, preferably with curved sides, and then calculate the volume, surface area and the work it would take to fill it.
• In Who Sucks the Most? students suck the water out of a cup and then measure the work it took and the horsepower of their sucking ability.

Others

• I love to have students build solids from formula descriptions.  In this flickr image, the students used Rice Crispy treats of two colors to show a solid with uniformed shaped cross sections.  This project description was used in an AP Calculus class. Rebecka Peterson also created solids herself and having her students do it. Bowman in Arabia describes a lesson where students look at and describe these types of solids before being given the mathematical description.
• In this Revolutionary Volume Lantern project, students create a model for a type of Chinese lantern, reproduce their model on DesMos, and calculate the volume of the lantern.  On this blog, Shireen Dadmehr explains her experience with this as an in-class project and gives recommendations for changes in the future.
• String spin shows the results of rotating a curve about an axis. Requires Java.