Session 48: The Fundamental Theorem of Calculus

OCW Scholar

Overview

Definite integrals "sum up" infinitesimal changes; one such change is adding the area of an infinitesimal rectangle. Another is traveling an infinitesimal distance forward. In this session we use definite integrals to compute distance traveled over time given a velocity function. We discuss negative integrands and then list a few properties of definite integrals.

Lecture Video and Notes

Video Excerpts

Flash and JavaScript are required for this feature.

» Clip 1: Interpretation of the Fundamental
Theorem (5 min)
» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: The Fundamental Theorem and Negative
Integrands (7 min)
» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

» Clip 3: Properties of Integrals (9 min)
» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

Worked Example

Integral of sin(x) + cos(x)

« Previous | Next »

MIT OpenCourseWare makes the materials used in the teaching of almost all of MIT's subjects available on the Web, free of charge. With more than 2,000 courses available, OCW is delivering on the promise of open sharing of knowledge.

Your use of the MIT OpenCourseWare site and materials is subject to our Creative Commons License and other terms of use.

Find courses by:

Collections

Cross-Disciplinary Topic Lists

Translated Courses

Session 48: The Fundamental Theorem of Calculus

Overview

Lecture Video and Notes

Video Excerpts

Worked Example

Courses

About

Donate

Featured Sites

Tools

About MIT OpenCourseWare

Our Corporate Supporters