# MAT-232-OL Module 2 - MAT-232 CALCULUS II Module...

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MAT-232: CALCULUS II Module 2—Integration Techniques, L'Hôpital's Rule, and Improper Integrals TOPICS Module 2 covers the following topics: using the new methods of integration when called for distinguishing which method is used for which integrals and, where more than one method works, which one is best using the necessary trigonometric identities to change the problem so that substitution can be used matching up particular integrals with particular methods of integration decomposing rational functions into partial fractions integrating the various kinds of partial fractions that can occur recognizing when you are dealing with irreducible quadratics and roots of multiplicity more than 1, and how the resulting decomposition proceeds applying L’Hôpital's Rule successively when needed recognizing how expressions must be modified so that L'Hôpital's Rule is applicable recalling and applying the basic properties of logarithms, exponentials, and trigonometric functions finding the areas of unbounded regions of two-dimensional space whenever the improper integrals converge handling all types of improper integrals with skills that involve methods of integration and finding all kinds of limits. STUDY MATERIALS Textbook Readings Study sections 6.2, 6.3, 6.4, 6.6, and 3.2 in the course textbook. Then read the Technical Commentary given below. Technical Commentary Copyright © 2016 by Thomas Edison State University. All rights reserved.
Read the following brief commentary topics for further explanations and notes on the material covered in this module. Following the commentary are video tutorials and suggested Self-Check Exercises. Be sure to work through these practice exercises to help solidify the skills learned in the module and to prepare for the module-ending written assignment. Integration by Parts Trigonometric Integrals Trigonometric Substitution Partial Fractions Indeterminate Forms and L'Hôpital's Rule Improper Integrals Video Tutorials Integration by Parts —Example Using Integration by Parts (YouTube video, 9:33 min.),