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Browse materialsMIT 18.01SC · 3. The Definite Integral and its Applications

Single Variable Calculus — 3. The Definite Integral and its Applications

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About this course

Source: MIT OpenCourseWare 18.01SC Single Variable Calculus, Fall 2010, Prof. David Jerison — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: this unit's sessions in MIT's listing order. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 22, 2026. How RedLectern is built.

Instructor: Prof. David Jerison
Term: Fall 2010
Level: Undergraduate
What's inside: 75 videos · 46 other files
Materials open: Videos here · files on MIT OCW

Other versions of this course

18.01 · Fall 2020 · On MIT OCW ↗
18.01SC · Fall 2010 · Study here (this version)
18.01 · Fall 2006 · Study here
18.01 · Fall 2005 · On MIT OCW ↗

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Start course: Clip 1: Introduction to Definite Integrals Find a topic

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Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Session 43: Definite Integrals

Session 44: Adding Areas of Rectangles

Session 45: Some Easy Integrals

Single Variable Calculus — 3. The Definite Integral and its Applications

Materials by section

Session 43: Definite Integrals

Session 44: Adding Areas of Rectangles

Session 45: Some Easy Integrals

Session 46: Riemann Sums

Session 47: Introduction of the Fundamental Theorem of Calculus

Session 48: The Fundamental Theorem of Calculus

Session 49: Applications of the Fundamental Theorem of Calculus

Session 50: Combining the Fundamental Theorem and the Mean Value Theorem

Problem Set 6

Session 54: The Second Fundamental Theorem and ln(x)

Session 55: Creating New Functions Using the Second Fundamental Theorem

Session 56: Geometric Interpretation of Definite Integrals

Session 57: How to Calculate Volumes

Session 58: Volume of a Sphere, Revolving About x-axis

Session 59: Volume of a Parabaloid, Revolving About y-axis

Problem Set 7

Session 60: Integrals and Averages

Session 61: Integrals and Weighted Averages

Session 63: Numerical Integration

Session 64: Numerical Integration, Continued

Problem Set 8

Session 67: Materials for Exam 3

Clip 1: Introduction to Definite Integrals

Clip 2: Definition of Definite Integrals

Clip 1: Example: f(x)= x2

Clip 2: Summation Notation

Summation Notation Practice

Clip 1: Simple Definite Integrals

Clip 2: Summary of Examples

Clip 1: Introduction to Riemann Sums

Riemann Sum

Clip 1: Example: Cumulative Debts

Computing the Volume of a Paraboloid

Diffusion of a Chemical

Clip 1: The First Fundamental Theorem of Calculus

Clip 2: Using the First Fundamental Theorem

Definite Integrals of tan (x)

Clip 1: Interpretation of the Fundamental Theorem

Clip 2: The Fundamental Theorem and Negative Integrands

Clip 3: Properties of Integrals

Clip 1: Example of Estimation

Clip 2: Example: Change of Variables

Definite Integral by Substitution

Clip 1: Substitution When u' Changes Sign

Clip 1: Review of the Fundamental Theorem

Clip 2: The Fundamental Theorem and the Mean Value Theorem

Clip 3: The Mean Value Theorem and Estimation

Clip 1: Second Fundamental Theorem of Calculus

Clip 2: Using the Second Fundamental Theorem of Calculus

Applying the Second Fundamental Theorem

Second Fundamental Theorem and Chain Rule

Second Fundamental Theorem and Quadratic Approximation

Clip 1: Proof of the Second Fundamental Theorem of Calculus

Clip 2: Proof of the First Fundamental Theorem of Calculus

Clip 1: Antiderivative of 1/x

Clip 2: Area Under the Bell Curve

Clip 1: Alternate Definition of Natural Log

Clip 2: Log of a Product

Clip 1: The Bell Curve

Clip 2: More New Functions from Old

Clip 1: Areas Between Curves

Clip 2: Example: Area Between x = y2 and y = x − 2

Area Between the Graphs of Sine and Cosine

Area Between y=x³ and y=3x-2