Notes on Calculus II

COURSE CONTENT /SUBJECT MATTER

Integral Calculus Cover Photo

I. The Differential

II. The Indefinite Integral

1. The Indefinite Integral

2. Basic Integration Formulas

3. Integration by Substitution

4. Integration of Trigonometric Functions

5. Integration of Exponential Functions

6. Integration of Hyperbolic Functions

7. Applications of Indefinite Integration

III. Methods of Integration

1. Product of Sines and Cosines

2. Powers of Sines and Cosines

3. Powers of Tangents and Secants

4. Powers of Cotangents and Cosecants

5. Trigonometric Substitutions

6. Additional Standard Formulas

7. Integrands Involving Quadratic Expressions

8. Algebraic Substitutions

9. Integration of Rational Functions of sin x and cos x

10. Integration by Parts

11. Integration of Rational Functions

IV. The Definite Integral

1. Summation Notation

2. The Definite Integral

3. Properties of the Definite Integral

4. Fundamental Theorem of Integral Calculus

V. Geometric Applications of the Definite Integral

1. Area Under the Curve

2. Area Between Two Curves

3. The area in Polar Coordinates

4. The volume of a Solid of Revolution

1. The Circular Disk Method

2. The Washer Method

3. The Cylindrical Shell Method

4. The Pappus Theorem

5. Volumes of Solids with Known Cross Sections

6. Length of an Arc

7. Area of Surface of Revolution

VI. Physical Applications of the Definite Integral

1. Force of a Fluid Pressure

2. Work

3. First Moment of Plane Area

4. The centroid of a Plane Area

5. The centroid of a Solid of Revolution

6. Moment of Inertia of a Plane Area

7. Moment of Inertia of a Solid of Revolution

VII. Double Integration

1. The Double Integral

2. The Iterated Integral

3. Plane Area

4. The volume of a Solid of Revolution

5. The centroid of a Plane Area

6. Moment of Inertia of a Plane Area