1 / 9

Simplifying Problems with Trigonometric Substitutions

Explore the concept of trigonometric substitutions in calculus, focusing on how right triangles and the Pythagorean theorem can simplify integrals. The process involves recognizing patterns, moving components to the hypotenuse, and employing double angle formulas. Completing the square is another critical technique we can use to achieve the necessary form for substitution. This approach is essential for solving complex problems effectively and understanding key formulas in mathematics, leading to quicker and more efficient problem-solving strategies.

dannon
Télécharger la présentation

Simplifying Problems with Trigonometric Substitutions

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. Photo by Vickie Kelly, 2004 Greg Kelly, Hanford High School, Richland, Washington Ch.8 Extra Topic: Trigonometric Substitutions Monticello (Thomas Jefferson’s home), Alexandria, VA

  2. 1 These are in the same form. We can use right triangles and the pythagorean theorem to simplify some problems.

  3. 1 We can use right triangles and the pythagorean theorem to simplify some problems. This is a constant.

  4. If the integral contains , we use the triangle at right. If we need , we move a to the hypotenuse. If we need , we move x to the hypotenuse. This method is called Trigonometric Substitution.

  5. 2 double angle formula

  6. 2 double angle formula

  7. We can get into the necessary form by completing the square. 5

  8. 6 Complete the square:

  9. Here are a couple of shortcuts that are result from Trigonometric Substitution: These are on your list of formulas. They are not really new. p

More Related