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Advanced Integration Techniques, L’Hopital’s Rule and Improper Integrals
Topic Review on "Title":
Integration by parts:
The way to get the mother functions by integration by parts.
If functions and are continuous at but the limit cannot be evaluated by substituting
Suppose that and exists, and that then
Integrals with infinite integrands:
Let be a continuous function on the interval which is unbounded as then
is called an improper integral with infinite integrand at b.
Rapid Study Kit for "Title":
Core Concept Tutorial
Problem Solving Drill
Review Cheat Sheet
"Title" Tutorial Summary :
Advanced integration techniques are introduced in this tutorial with the help of examples and integration methods. Tables of basic integration techniques are introduced with example problems. Strategies to calculate complicated integrals are given to show the integration by parts idea.
The rationale behind integration by parts is shown to present tabular integration. Different types of integrals involving sines and cosines are shown in some of the example problems. The products of sines and cosines are given with different types of scenarios. Trigonometric substitutions are given to calculate integrals involving trigonometric functions.
Specific Tutorial Features:
Several example problems with step by step illustrations of solutions.
Tables and graphs shown the different types of integration scenarios and important formulas.
Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
Definition slides introduce terms as they are needed.
Visual representation of concepts
Animated examples—worked out step by step
A concise summary is given at the conclusion of the tutorial.
"Title" Topic List:
Basic formulas and integration methods Basic integration rules (I) Basic integration rules (II) Integration by parts Tabular integration Products of sines and cosines Trigonometric substitutions Partial fractions and rational functions Using integral tables and reduction formulas Indeterminate forms and L’Hopital’s Rule Improper Integrals