Riemann Sums, Definite Integrals, Fundamental Theorem of Calculus, AP Calculus I/AB

Riemann Sums, Definite Integrals, Fundamental Theorem of Calculus

VI. Integrals: Lecture 2 | 22:02 min

AP Calculus I/AB > Riemann Sums, Definite Integrals, Fundamental Theorem of Calculus

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Geometrically, Riemann sums represent sums of rectangle approximations.
The definite integral is a limit of Riemann sums.
For very simple functions, it is possible to directly compute Riemann sums and then take the limit.
Though this topic is very important theoretically, in practice we will compute integrals by using the First Fundamental Theorem of Calculus.

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I. Overview of Functions
	Review of Functions	26:29
	Compositions of Functions	12:29
II. Limits
	Average and Instantaneous Rates of Change	20:59
	Limit Investigations	22:37
	Algebraic Evaluation of Limits	28:19
	Formal Definition of a Limit	23:39
	Continuity and the Intermediate Value Theorem	19:09
III. Derivatives, part 1
	Limit Definition of the Derivative	22:52
	The Power Rule	26:01
	The Product Rule	14:54
	The Quotient Rule	19:17
	Applications of Rates of Change	17:43
	Trigonometric Derivatives	26:58
	The Chain Rule	23:47
	Inverse Trigonometric Functions	27:05
	Equation of a Tangent Line	15:52
IV. Derivatives, part 2
	Implicit Differentiation	30:05
	Higher Derivatives	13:16
	Logarithmic and Exponential Function Derivatives	17:42
	Hyperbolic Trigonometric Function Derivatives	14:30
	Related Rates	29:05
	Linear Approximation	23:52
V. Application of Derivatives
	Absolute Minima and Maxima	18:57
	Mean Value Theorem and Rolle's Theorem	20:00
	First Derivative Test, Second Derivative Test	27:11
	L'Hopital's Rule	23:09
	Curve Sketching	40:16
	Applied Optimization	25:37
	Newton's Method	25:13
VI. Integrals
	Approximating Areas and Distances	36:50
	Riemann Sums, Definite Integrals, Fundamental Theorem of Calculus	22:02
	Substitution Method for Integration	23:19
VII. Application of Integrals, part 1
	Area Between Curves	19:59
	Volume by Method of Disks and Washers	24:22
	Volume by Method of Cylindrical Shells	30:29
	Average Value of a Function	16:31
VIII. Extra
	Graphs of f, f', f''	23:58
	Slope Fields for Differential Equations	18:32
	Separable Differential Equations	17:04