Intuition of Integration by Substitution Activity

Abstract

Integration by substitution is the first strategy in a standard set of integration techniques covered in most Calculus sequences (either at the end of Calculus I or at the beginning of Calculus II). This activity is designed to introduce students to the strategy and help them develop a big picture intuition of what is going on to make subsequent calculation details more meaningful. Students review composite functions and the chain rule in the context of an application. Students are then guided through the process of substitution while actively reflecting on its connection to the reviewed material.

Level: High School/Undergraduate

Setting: classroom

Activity Type: learning cycle

Discipline: mathematics

Course: single variable calculus.