**Author** David Graser, Yavapai College, Prescott, AZ (David_Graser@yc.edu)

**Abstract**

Like the Total Cost to Produce Turbo Blenders project, this project requires the student to compute total change from rate information. In this project, the rate function is given as a formula and total change can be estimated from left and right sums or computed exactly using the Fundamental Theorem of Calculus.

- Content Area – Area, left and right sums, fundamental theorem of calculus, substitution method
- Time Frame – 2 to 3 weeks with mini-lectures
- Published – November 3, 2010
- Keywords – area, left and right sums, fundamental theorem of calculus, substitution method

**Project Content**

**Scaffolding Resources**

**Handout: Substitution Method** (DOC | PDF)

**Notes**

- The solution to this project can be estimated with left and right sums or calculated exactly using the substitution method and the Fundamental Theorem of Calculus. I like to see my students do both and then comment on whether the numbers are consistent.