L'HOPITAL'S RULE, IMPROPER INTEGRALS, PARTIAL FRACTIONS
· Basic Integration Rules
· Integration by Parts
o Good information on integration by parts with examples
§ Integration by Parts
§ More integration by parts
o Problems on Integration by Parts with examples
§ More problems on Integration by Parts
o Integration by Parts applet
o Integrals of trigonometric functions, including integration by parts
o Find the error - Part I
§ Find the error - Part II
· Trigonometric Integrals (more complex ones)
o Integrating Rational Expressions of Trigonometric Functions
o Integrating Powers & Products of sines and cosines
o More on products of sines and cosines
o Integrating Trigonometric Functions
§ Integration of trigonometric functions -- examples and problems to try
§ Integrals of trigonometric functions
§ Trigonometric Integrals
§ Find the error
· Trigonometric Substitution
o Trigonometric Substititutions
o Trigionometric Substitution
· Partial Fractions
o Partial Fraction Decompositions
o Integration of Rational Functions
o Problems using partial fractions
o More problems using partial fractions
o Population Growth
§ Discussion of logistic equations
§ Logistic problem about harvesting fish
· Integration by Tables and Other Integration Techniques
· Indeterminate Forms and L'Hopital's Rule
o L'Hopital's Rule explained
o Indeterminant Forms
§ Indeterminant Quotient Forms
§ Other Indeterminant Quotient Forms
o Problems using L'Hopital's Rule
§ More problems using L'Hopital's Rule
§ L'Hopital's Rule problems, solutions, and explanations
§ L'Hopital's Rule
o Applet illustrating L'Hopital's rule
§ L'Hopital's Rule applet
o Review problems on L'Hopital's Rule--Go to Calculus Book I, then Applications of the Derivative, then L'Hopital's Rule
o Find the error
· Improper Integrals
o Improper Integrals -- Introduction
o Convergence and Divergence of Improper Integrals
o Problems on improper integrals
o More improper integrals
o Problems on Improper Integrals
o Tests of Convergence for Improper Integrals
o Improper Integrals
o Improper integrals applet
· Other Methods of Integration
o Power Substitution
o Reduction Formulas
· Summaries and Review Problems
o Further Integration Techniques and Applications of the Integral Summary