1 / 5

Strategies for Integrating Functions Effectively

Learn effective integration strategies such as simplifying the integrand, u-substitution, trigonometric functions, partial fractions, integration by parts, radical substitutions, and manipulation of the integrand. Experiment with various techniques to tackle integration challenges.

arthurlong
Download Presentation

Strategies for Integrating Functions Effectively

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 8.5 Strategy for Integration

  2. HINT1 Simplify the integrand if possible.

  3. HINT 2 Look for an obvious u-substitution.

  4. HINT 3 Classify the integrand according to form. • Trigonometric Functions: Use the techniques of Section 8.2 • Rational Functions: Use the technique of Partial Fractions (Section 8.4). • Integration by Parts: Try Integration by Parts if there are two functions multiplied. • Radicals: • Square roots with radicand of the form ±x2 ± a2 require trigonometric substitution (Section 8.3) • nth root with a radicand of the form ax + b can usually be solved by using the rationalizing substitution

  5. HINT 4 Try again. • Try substitution. Some substitutions are not obvious. • Try parts even if the problem does not look like parts will work. It may work. • Manipulate the integrand. Many times this involves multiplying the numerator and denominator by the same term. • Try to relate the problem to previous problems. • Use several integration techniques in the same problem.

More Related