Trigonometric Substitution

1 / 10

# Trigonometric Substitution - PowerPoint PPT Presentation

Trigonometric Substitution. Lesson 8.4. 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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Trigonometric Substitution' - rea

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Trigonometric Substitution

Lesson 8.4

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

Use identitytan2x + 1 = sec2x

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

θ

3

x

Finishing Up
• Our results are in terms of θ
• We must un-substitute back into x
• Use the triangle relationships
Try It!!
• For each problem, identify which substitution and which triangle should be used
Keep Going!
• Now finish the integration
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
Special Integration Formulas
• Useful formulas from Theorem 8.2
• Look for these patterns and plug in thea2 and u2 found in your particular integral
Assignment
• Lesson 8.4
• Page 550
• Exercises 1 – 45 EOOAlso 67, 69, 73, and 77