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Trigonometric Substitutions Trigonometric Substitutions

Trigonometric Substitutions - PowerPoint Presentation

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Trigonometric Substitutions - PPT Presentation

Section 84b How do we evaluate this integral Trigonometric Substitutions These trigonometric substitutions allow us to replace b inomials of the form b y single squared terms and thereby transform a number ID: 509718

trigonometric substitutions triangles evaluate substitutions trigonometric evaluate triangles followingreference based common eplaces set integrals

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Slide1

Trigonometric Substitutions

Section 8.4bSlide2

How do we evaluate this integral?

Trigonometric Substitutions

These trigonometric substitutions allow us to replace

b

inomials of the form

b

y single squared terms, and thereby transform a number

o

f integrals (like the one above) into ones we can evaluate

d

irectly or find in a table of integrals.Slide3

The most common substitutions are based on the following

r

eference triangles:

Trigonometric Substitutions

WithSlide4

The most common substitutions are based on the following

r

eference triangles:

Trigonometric Substitutions

WithSlide5

The most common substitutions are based on the following

r

eference triangles:

Trigonometric Substitutions

WithSlide6

1. r

eplaces with

Trigonometric Substitutions

2.

r

eplaces with

3.

r

eplaces with

Also, we want any substitution to be reversible so we can

c

hange back to the original variable afterward. For example:

requires

with

Essentially, keep positives

with any absolute values…Slide7

Trigonometric Substitutions

Evaluate

SetSlide8

Trigonometric Substitutions

Evaluate

SetSlide9

Trigonometric Substitutions

Evaluate

Appendix A7, Formula 88 (p.631)Slide10

Trigonometric Substitutions

EvaluateSlide11

Trigonometric Substitutions

Evaluate