#### Title

Investigating the fundamental theorem of calculus

#### Document Type

Article

#### Publication Date

2010

#### Abstract

The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were reasonably successful with students. However, she was dissatisfied with the level of her students' understanding of the theorem and reflected that they would need to understand that an integral with a variable upper limit is a function. In this article, the author shares how she was inspired to create a lesson on the fundamental theorem of calculus that drew on students' current understanding of definite integrals and allowed them to develop the understanding that an integral with a variable upper limit is a function. A student's response to the lesson on the fundamental theorem of calculus expands the lesson to include representing accumulated area as a function.

#### Recommended Citation

Johnson, H. L. (2010). Investigating the fundamental theorem of calculus. Mathematics Teacher, 103(6), 430-435.