Integrals
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Antiderivatives (7:42)
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Antiderivatives and Integration (10:10)
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Notation for Integration (12:19)
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The Power Rule (14:39)
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Integratable Form (10:40)
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Indefinite and Definite Integrals (6:46)
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Evaluating Definite Integrals (13:33)
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Riemann Sums (9:52)
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Integrals and Riemann Sums (7:42)
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The Fundamental Theorem of Calculus (13:01)
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Practice Questions
Integration Techniques
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Integration by U-Substitution (18:09)
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The Reverse Chain Rule (11:06)
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Integration by Parts (17:59)
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Integration by Parts for Definite Integrals (14:49)
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Integration using Partial Fractions (35:20)
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Integrating the Sine and Cosine Functions (8:46)
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Integrating the Tangent Function (7:49)
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Integrals Involving Exponential and Logarithmic Functions (11:17)
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Improper Integrals (16:29)
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Evaluating Improper Integrals of the Form [a, infinity) (11:33)
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Evaluating Improper Integrals of the Form (- infinity, infinity) (13:46)
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Evaluating Improper Integrals - Discontinuous at ‘a’ or ‘b’ (10:47)
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Improper Integrals – Discontinuous in the interval (a, b) (14:50)
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Practice Questions
Application of Integrals
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Finding the Area Under a Curve (16:51)
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Finding the Area Between Two Curves (18:59)
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Volumes of Revolution (9:53)
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Volumes of Revolution Around the X-Axis (11:57)
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Volumes of Revolution Around the Y-Axis (16:44)
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Arc Length Using Integration (9:09)
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Evaluating Arc Length Using Integration (19:56)
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Practice Questions
Parametric Functions
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Parametric Functions (10:14)
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Writing Parametric Functions in Cartesian Form (15:38)
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Differentiating Parametric Functions (13:26)
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Second Derivatives for Parametric Functions (15:30)
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Curves of Parametric Functions (15:52)
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Tangent Lines to Parametric Curves (17:46)
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The Area Under a Parametric Curve (13:42)
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The Arc Length of a Parametric Curve (29:52)
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Volumes of Revolution for Parametric Curves (13:33)
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Surface Area of Revolution for Parametric Curves (11:50)
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Practice Questions
Polar Functions
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Polar Co-ordinates (8:35)
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Switching Between Polar and Cartesian Co-ordinates (16:34)
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Graph Sketching for Polar Curves (32:38)
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Tangent Lines to Polar Curves (28:12)
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The Intersection of Polar Curves (20:36)
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The Area Bounded by a Polar Curve (14:43)
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The Arc Length of a Polar Curve (18:48)
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The Surface Area of Revolution of a Polar Curve (16:07)
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Practice Questions
Sequences
Series
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Partial Sums of an Infinite Series (11:51)
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Sum of an Infinite Series Using Partial Sums (22:26)
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Geometric Series Convergence Test (16:15)
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The Sum of a Geometric Series (16:12)
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Repeating Decimal Problems (7:52)
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Telescoping Series (26:17)
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The Sum of a Convergent Telescoping Series (11:34)
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The Limit and Sum of an Infinite Series (9:28)
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Common Series Results (12:50)
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Practice Questions
Series Convergence Tests
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The Integral Convergence Test (17:56)
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The P-Series Test (12:45)
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The Nth Term Test (16:19)
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The Direct Comparison Test (14:19)
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The Limit Comparison Test (15:44)
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The Ratio Test (17:49)
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The Root Test (17:20)
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Absolute and Conditional Convergence (17:19)
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Alternating Series Test (20:20)
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Alternating Series Estimates (12:30)
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Practice Questions
Power Series
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Starting Power Series (7:18)
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Power Series, Taylor Series and Maclaurin Series (9:49)
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Radius and Interval of Convergence (10:18)
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Multiplying Power Series (14:51)
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Differentiating Power Series (7:43)
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Evaluating Indefinite Integrals for Power Series (10:52)
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Evaluating Definite Integrals for Power Series (10:34)
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Starting Maclaurin Series (16:59)
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Evaluating the Sum of a Maclaurin Series (8:32)
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The Radius and Interval of Convergence of a Maclaurin Series (26:22)
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Writing Indefinite Integrals as an Infinite Series (8:31)
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Approximating Definite Integrals Using an Infinite Series (24:02)
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Starting Taylor Series (13:52)
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The Radius and Interval of Convergence of a Taylor Series (24:33)
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Practice Questions
Additional Resources
