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
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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