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Calculus with Analytic Geometry
Calculus of a Single Variable
Multivariable Calculus, Seventh Edition
Ron Larson - The Pennsylvania State University, The Behrend
College
Robert P. Hostetler - The Pennsylvania State University, The Behrend College
Bruce H. Edwards - University of Florida | | |
| | Chapter Summary
Chapter 7: Integration Techniques, L'Hôpital's Rule, and Improper Integrals
7.1
- Review procedures for fitting an integrand to one of the basic integration rules.
7.2
- Find an antiderivative using integration by parts.
- Use a tabular method to perform integration by parts.
7.3
- Solve trigonometric integrals involving powers of sine and cosine.
- Solve trigonometric integrals involving powers of secant and tangent.
- Solve trigonometric integrals involving sine-cosine products with different angles.
7.4
- Use trigonometric substitution to solve an integral.
- Use integrals to model and solve real-life applications.
7.5
- Understand the concept of partial fraction decomposition.
- Use partial fraction decomposition with linear factors to integrate rational functions.
- Use partial fraction decomposition with quadratic factors to integrate rational functions.
7.6
- Evaluate an indefinite integral using a table of commands.
- Evaluate an indefinite integral using reduction formulas.
- Evaluate an indefinite integral involving rational functions of sine and cosine.
7.7
- Recognize limits that produce indeterminate forms.
- Apply L’Hôpital’s Rule to evaluate a limit.
7.8
- Evaluate an improper integral that has an infinite limit of integration.
- Evaluate an improper integral that has an infinite discontinuity.
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