Part 4 - Integrals - Video 1
Section 1: Antiderivatives, Indefinite Integrals
Lesson 1: Antiderivatives and Integrals (48:44)

We "think backwards" to find a function with a given derivative (0:37). Next the definition of antiderivative; including power functions, trig functions, and exponentials (7:50). The integral sign represents the antiderivative (31:10).

Part 4 - Integrals - Video 3
Section 1: Antiderivatives, Indefinite Integrals
Lesson 3: Properties of Indefinite Integrals (53:45)

Review of antiderivatives (0:38). We discover the constant multiple rule for Integrals (12:12). From properties of derivatives we deduce the sum rule (23:54). Finally a few polynomial examples (29:28).

Part 4 - Integrals - Video 4
Section 1: Antiderivatives, Indefinite Integrals
Lesson 4: Integral Formulas (44:46)

We begin with exponential and log Integrals (0:38). We move to trigonometry and inverse trig integrals (12:55). Examples follow with trig-based and rational functions (24:00).

Part 4 - Integrals - Video 5
Section 2: Areas and Riemann Sums
Lesson 1a: The Right- and Left-Hand Rules (28:36)

Introduction to areas (0:38). We use rectangles to approximate areas (7:38). Some sums used are the right-hand rule (9:47) and the left-hand rule (20:06).

Part 4 - Integrals - Video 6
Section 2: Areas and Riemann Sums
Lesson 1b: The Right- and Left-Hand Rules (41:30)

More accurate ways of approximating areas (0:38). Reducing the error (18:25). Definition of exact area using limits (33:48).

Part 4 - Integrals - Video 7
Section 2: Areas and Riemann Sums
Lesson 2a: Definition of Area, Riemann Sums (38:37)

A look at general right-hand sums using n rectangles (0:44). Defining the exact area under a curve (8:56). Using the left-hand rule for areas (16:34).

Part 4 - Integrals - Video 9
Section 2: Areas and Riemann Sums
Lesson 3: Sigma Notation for Sums (49:46)

Introducing the Sigma Notation (0:40). How to rewrite common sums in sigma notation, from i=1 to n (18:50). We rewrite our areas as sums of rectangles using the sigma notation (33:40).

Part 4 - Integrals - Video 10
Section 3: Fund Thm of Calc, Definite Integrals
Lesson 1a: The Fundamental Theorem (36:16)

We find the area under n rectangles (0:40). Then the fundamental theorem of calculus (16:31). This solves a very tricky limit (28:50). Finally, different antiderivatives (31:10).

Part 4 - Integrals - Video 12
Section 3: Fund Thm of Calc, Definite Integrals
Lesson 2: A "Proof" of the Fund Theorem (1:00:50)

First, a short derivative review (0:41). Picture proof of the fund thm (3:39). Examples using the fund thm (23:14). What's wrong with this example? (50:14).

Part 4 - Integrals - Video 13
Section 3: Fund Thm of Calc, Definite Integrals
Lesson 3a: Geometry of Fund Theorem (37:45)

Extending the definite integral (0:42). Properties of definite integrals: no-interval rule (8:24), backwards intervals (12:20), constant multiple (16:12), sum (20:10), combined interval rules (22:25).