## Topic outline

- CALCULUS VOLUME 2 COURSECALCULUS VOLUME 2 COURSE
This comprehensive course contains 7 sections with 50 self-grading lessons, including final assessments. The first section is available to try for free.

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- IntegrationIntegration
- Use sigma (summation) notation to calculate sums and powers of integers.
- Use the sum of rectangular areas to approximate the area under a curve.
- Use Riemann sums to approximate area.

- State the definition of the definite integral.
- Explain the terms integrand, limits of integration, and variable of integration.
- Explain when a function is integrable.
- Describe the relationship between the definite integral and net area.
- Use geometry and the properties of definite integrals to evaluate them.
- Calculate the average value of a function.

1.3. The Fundamental Theorem of Calculus

1.4. Integration Formulas and the Net Change Theorem

1.5. Substitution

1.6. Integrals Involving Exponential and Logarithmic Functions

1.7. Integrals Resulting in Inverse Trigonometric FunctionsClick the link above to get the access codes and instructions to add this trial course to your LMS.

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- Integration - Final AssessmentIntegration - Final Assessment
This is the final assessment for

. (Available when you subscribe.)*Integration* - Subscribe & Try the FULL COURSE FREE for 14 days!This topicSubscribe & Try the FULL COURSE FREE for 14 days!
The full course includes all 50 lessons, including 7 Final Assessments with Instructor Answer Keys.

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- Applications of IntegrationApplications of Integration
2.1. Areas between Curves

2.2. Determining Volumes by Slicing

2.3. Volumes of Revolution: Cylindrical Shells

2.4. Arc Length of a Curve and Surface Area

2.5. Physical Applications

2.6. Moments and Centers of Mass

2.7. Integrals, Exponential Functions, and Logarithms

2.8. Exponential Growth and Decay

2.9. Calculus of the Hyperbolic Functions

Final Assessment - Techniques of IntegrationTechniques of Integration
3.1. Integration by Parts

3.2. Trigonometric Integrals

3.3. Trigonometric Substitution

3.4. Partial Fractions

3.5. Other Strategies for Integration

3.6. Numerical Integration

3.7. Improper Integrals

Final Assessment - Introduction to Differential Equations Introduction to Differential Equations
4.1. Basics of Differential Equations

4.2. Direction Fields and Numerical Methods

4.3. Separable Equations

4.4. The Logistic Equation

4.5. First-order Linear Equations

Final Assessment - Sequences and SeriesSequences and Series
5.1. Sequences

5.2. Infinite Series

5.3. The Divergence and Integral Tests

5.4. Comparison Tests

5.5. Alternating Series

5.6. Ratio and Root Tests

Final Assessment - Power SeriesPower Series
6.1. Power Series and Functions

6.2. Properties of Power Series

6.3. Taylor and Maclaurin Series

6.4. Working with Taylor Series

Final Assessment - Parametric Equations and Polar CoordinatesParametric Equations and Polar Coordinates
7.1. Parametric Equations

7.2. Calculus of Parametric Curves

7.3. Polar Coordinates

7.4. Area and Arc Length in Polar Coordinates

7.5. Conic Sections

Final Assessment - Subscribe for as low as $199 per yearSubscribe for as low as $199 per year
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