1 / 9

Trigonometric Substitution

Trigonometric Substitution. Lesson 9.6. a. x. New Patterns for the Integrand. Now we will look for a different set of patterns And we will use them in the context of a right triangle Draw and label the other two triangles which show the relationships of a and x. θ. 3. x.

alisa-ramsey
Download Presentation

Trigonometric Substitution

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. Trigonometric Substitution Lesson 9.6

  2. a x New Patterns for the Integrand • Now we will look for a different set of patterns • And we will use them in the context of a right triangle • Draw and label the other two triangles which show the relationships of a and x

  3. θ 3 x Use identitytan2x + 1 = sec2x Example • Given • Consider the labeled triangle • Let x = 3 tan θ (Why?) • And dx = 3 sec2θ dθ • Then we have

  4. θ 3 x Finishing Up • Our results are in terms of θ • We must un-substitute back into x • Use the triangle relationships

  5. Knowing Which Substitution u u

  6. Try It!! • For each problem, identify which substitution and which triangle should be used

  7. Keep Going! • Now finish the integration

  8. Application • Find the arc length of the portion of the parabola y = 10x – x2 that is above the x-axis • Recall the arc length formula

  9. Assignment • Lesson 9.6 • Page 386 • Exercises 1 – 33 (every other odd)Also 37, 39, and 41

More Related