Course Materials
Lessons
Indefinite Integration by Recognition
- Video - Reverse Chain Rule (7:06)
- Video - Integration by Recognition: Using Derivative of Exponential Functions (3:45)
- Video - Integration by Recognition using Derivative of Sine Function (3:32)
- Video - Integration by Recognition using Derivative of Cosine Function (4:20)
- Video - Integration by Recognition using Derivative of Tangent Function (4:16)
- Video - Integration by Recognition: Using Derivative of Logarithmic Functions (4:10)
- Video - Integration by Recognition using Product Rule (6:16)
- Video - Integration by Recognition using Long Division (7:22)
- Video - Integration of cosec x by Recognition involving Log TAN (4:18)
- Video - Integration of sec x by Recognition (4:52)
Integration by Substitution
- Video - Integration using Substitutions 1 (3:45)
- Video - Integration using Substitutions 2 (3:05)
- Video - Integration using Substitutions 3 (2:06)
- Video - Removal of Pronumerals 1 (4:39)
- Video - Removal of Pronumerals 2 (2:28)
- Video - Removal of Pronumerals 3 (2:43)
- Topic - Integration by Substitution: Basic
- Topic - Integration by Substitution: Surds
- Topic - Integration by Substitution: Rational Expressions
Integration using Substitution in Right-Angled Triangles
- Video - Integration using Substitution in Right-Angled Triangles 1 (3:11)
- Video - Integration using Substitution in Right-Angled Triangles 2 (1:54)
- Video - Integration using Substitution in Right-Angled Triangles 3 (4:58)
- Video - Integration using Substitution in Right-Angled Triangles 4 (1:54)
- Video - Integration using Substitution in Right-Angled Triangles 5 (3:16)
Definite Integrals
- Video - Theory of Definite Integrals (5:46)
- Video - Evaluating Plain Definite Integrals (4:56)
- Video - Evaluating Definite Integrals of Higher Orders (8:05)
- Video - Differentiating Definite Integrals (4:38)
- Video - Finding Unknown Limits of Definite Integrals (5:00)
- Video - Finding Unknowns of Expressions involving Definite Integrals (4:54)
- Video - Definite Integrals of Power Functions (5:22)
- Video - Definite Integrals involving Simplifications (3:47)
- Video - Definite Integrals Backwards (1:58)
- Video - Definite Integrals of Odd Functions (2:59)
- Video - Definite Integrals of Even Functions (4:47)
- Video - Integration of Even & Odd Functions (1:12)
Differentiation of Inverse Sine Function
- Video - Differentiation Formula of Inverse Sine Function (2:06)
- Video - Proof of Differentiation of Inverse Sine Function (2:48)
- Video - Differentiation of Inverse Sine Function (1:37)
- Video - Differentiation of Inverse Sine Function involving Chain Rule (2:36)
- Video - Differentiation of Inverse Sine Function involving Product Rule (1:38)
- Video - Differentiation of Inverse Sine Function involving Exponential Function (1:00)
- Video - Differentiation of Inverse Sine Function involving Reciprocal Function (1:36)
- Topic - Proving Differentiation of Inverse Sine
- Topic - Differentiation of Inverse Sine involving Chain Rule 1
- Topic - Differentiation of Inverse Sine involving Chain Rule 2
- Topic - Differentiation of Inverse Sine involving Chain Rule 3
- Topic - Differentiation of Inverse Sine involving Chain Rule 4
- Topic - Differentiation of Inverse Sine involving Chain Rule 5
- Topic - Differentiation of Inverse Sine involving Chain Rule 6
- Topic - Differentiation of Inverse Sine involving Chain Rule 7
Differentiation of Inverse Cosine Function
- Video - Differentiation Formula of Inverse Cosine Function (2:12)
- Video - Proof of Differentiation of Inverse Cosine Function (1:50)
- Video - Differentiation of Inverse Cosine Function (1:25)
- Video - Differentiation of Inverse Cosine Function involving Chain Rule (1:51)
- Video - Differentiation of Inverse Cosine Function involving Surds (1:48)
- Video - Differentiation of Inverse Cosine Function involving Sine Function (1:34)
- Topic - Proving Differentiation of Inverse Cosine
- Topic - Differentiation of Inverse Cosine involving Chain Rule 1
- Topic - Differentiation of Inverse Cosine involving Chain Rule 2
- Topic - Differentiation of Inverse Cosine involving Chain Rule 3
- Topic - Differentiation of Inverse Cosine involving Chain Rule 4
- Topic - Differentiation of Inverse Cosine involving Chain Rule 5
- Topic - Differentiation of Inverse Cosine involving Chain Rule 6
- Topic - Differentiation of Inverse Cosine involving Chain Rule 7
Differentiation of Inverse Tangent Function
- Video - Differentiation Formula of Inverse Tangent Function (2:27)
- Video - Proof of Differentiation of Inverse Tangent Function (1:31)
- Video - Differentiation of Inverse Tangent Function (1:40)
- Video - Differentiation of Inverse Tangent Function involving Chain Rule (3:43)
- Video - Differentiation of Inverse Tangent Function involving Logarithmic Function (2:27)
- Video - Differentiation of Inverse Tangent Function involving Sine Function (1:41)
- Topic - Proving Differentiation of Inverse Tangent
- Topic - Differentiation of Inverse Tangent involving Chain Rule 1
- Topic - Differentiation of Inverse Tangent involving Chain Rule 2
- Topic - Differentiation of Inverse Tangent involving Chain Rule 3
- Topic - Differentiation of Inverse Tangent involving Chain Rule 4
- Topic - Differentiation of Inverse Tangent involving Chain Rule 5
- Topic - Differentiation of Inverse Tangent involving Chain Rule 6
- Topic - Differentiation of Inverse Tangent involving Chain Rule 7
Integration of Inverse Sine Function
- Video - Indefinite Integration of Inverse Sine Function (3:33)
- Video - Definite Integration of Inverse Sine Function (1:31)
- Topic - Indefinite Integration of Inverse Sine 1
- Topic - Indefinite Integration of Inverse Sine 2
- Topic - Indefinite Integration of Inverse Sine 3
- Topic - Indefinite Integration of Inverse Sine 4
- Topic - Indefinite Integration of Inverse Sine 5
- Topic - Definite Integration of Inverse Sine 1
- Topic - Definite Integration of Inverse Sine 2
Integration of Inverse Cosine Function
- Video - Indefinite Integration of Inverse Cosine Function (5:48)
- Video - Definite Integration of Inverse Cosine Function (3:15)
- Topic - Indefinite Integration of Inverse CosIne 1
- Topic - Indefinite Integration of Inverse CosIne 2
- Topic - Indefinite Integration of Inverse CosIne 3
- Topic - Indefinite Integration of Inverse CosIne 4
- Topic - Indefinite Integration of Inverse CosIne 5
- Topic - Definite Integration of Inverse CosIne 1
- Topic - Definite Integration of Inverse CosIne 2
Integrations Resulted Inverse Tangent Functions
- Video - Indefinite Integrations resulted Inverse Tangent Function (4:18)
- Video - Indefinite Integrations resulted Inverse Tangent Function by Substitution (3:16)
- Topic - Indefinite Integration of Inverse Tangent 1
- Topic - Indefinite Integration of Inverse Tangent 2
- Topic - Indefinite Integration of Inverse Tangent 3
- Topic - Indefinite Integration of Inverse Tangent 4
- Topic - Indefinite Integration of Inverse Tangent 5
- Topic - Definite Integration of Inverse Tangent
Area Under a Curve
- Video - Theory of Area under Curves (4:17)
- Video - Area under Curves given Domains (6:09)
- Video - Area between Curves and Axes (5:01)
- Video - Signed Area (5:47)
- Video - Combined Positive and Negative Areas (5:09)
- Video - Positive and Negative Areas by Sketching Curves (4:00)
- Video - Theory of Area under Trigonometric Curves (2:58)
- Video - Finding the Area under Sine Curves (5:28)
- Video - Finding the Area under Cosine Curves (3:12)
Area between Two Functions
- Video - Area between Two Curves 1 (3:56)
- Video - Area between Two Curves 2 (6:24)
- Video - Area between Two Curves 3 (3:09)
- Video - Signed Area between Two Curves (4:39)
- Video - Combined Signed Areas between Two Curves 1 (6:43)
- Video - Combined Signed Areas between Two Curves 2 (8:49)
- Video - Finding Area between Sine Curve & a Straight Line (10:44)
- Video - Finding the Area between Sine and Cosine Curves (7:15)
Kinematics using Integration
- Video - Expression of the Distance using Integration (2:23)
- Video - Working with Velocity in Trigonometric Functions (3:11)
- Video - Working with Acceleration in Natural Exponential Functions (5:12)
- Video - Maximum Speed using Acceleration 1 (5:38)
- Video - Maximum Speed using Acceleration 2 (2:54)
- Video - Changes in Displacement and Velocity (2:57)
Volumes using Integration
- Video - Volumes Rotated about x-axis 1 (4:43)
- Video - Volumes Rotated about the y-axis (5:58)
- Video - Volumes Rotated about x-axis and y-axis (5:48)
- Video - Finding the Volume involving Trigonometric Functions (4:13)
- Topic - Volume of Revolution bounded by Straight Lines & x-axis
- Topic - Volume of Revolution bounded by Semi-Circles & x-axis
- Topic - Volume of Revolution bounded by Surd Graphs & y-axis
- Topic - Volume of Revolution bounded by Parabolas & x-axis
- Topic - Volume of Revolution bounded by Parabolas & y-axis
- Topic - True/False of Expression of Volumes Rotating the X-axis
- Topic - True/False of Expression of Volumes Rotating the Y-axis
Volumes for Two Functions
- Video - Volumes Rotated about x-axis 2 (5:44)
- Video - Volumes between Two Curves (5:13)
- Topic - Volume of Revolution between Horizontal Lines & Parabolas
- Topic - Volume of Revolution between Straight Lines & Parabolas
- Topic - Volume of Revolution between Straight Lines & Surd Graphs
- Topic - Volume of Revolution about y-axis between Parabolas & Surd Graphs
- Topic - Half Volume of Revolution between Parabolas & Surd Cubic Graphs
- Topic - Volume of Revolution between Parabolas
First Order Differential Equations
- Topic - General Solutions of dy/dx = f(x) Polynomial Functions
- Topic - General Solutions of dy/dx = f(x) Exponential Functions
- Topic - General Solutions of dy/dx = f(x) Surd Functions
- Topic - General Solutions of dy/dx = f(x) Trigonometric Functions
- Topic - Particular Solutions of dy/dx = f(x) Substitution Method
- Topic - Particular Solutions of dy/dx = f(x) Multiple Choice
Slope Fields or Direction Field
- Topic - General Solutions of dy/dx = g(y) Polynomials
- Topic - General Solutions of dy/dx = g(y) Trigonometric Functions
- Topic - Particular Solutions of dy/dx = g(y) Inverse Sine Functions
- Topic - General Solutions of dy/dx = g(y) Exponential Functions
- Topic - General Solutions of dy/dx = g(y) Square Root Functions
- Topic - Particular Solutions of dy/dx = g(y) Surd Functions
