18.01SC | Fall 2010 | Undergraduate

Single Variable Calculus

Part A: Definition of the Definite Integral and First Fundamental Theorem

Session 48: The Fundamental Theorem of Calculus

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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

Clip 1: Interpretation of the Fundamental Theorem

Clip 2: The Fundamental Theorem and Negative Integrands

Clip 3: Properties of Integrals

Worked Example

Integral of sin(x) + cos(x)

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Course Info

As Taught In
Fall 2010
Learning Resource Types
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Recitation Videos