Tigonomthstthion - University of California, Berkeleyapaulin/1BTrigonometricSubstitution.pdfr Tiz z...
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Tigonomthstthion Him Integrate certain algebraic Functions by exploiting trigonometric identities Example Area at a circle a r positive ILE DE c because t Observation x r since V r s O da dy r cos 0 da ran so do r Tiz z JEE d z J r TO DO r z Iz the er J t z do e Iz O since I Z TIM z Awesome
Transcript of Tigonomthstthion - University of California, Berkeleyapaulin/1BTrigonometricSubstitution.pdfr Tiz z...
TigonomthstthionHim Integrate certain algebraic Functions
by exploiting trigonometric identities
Example Area at a circle
a
r
positiveILE DE c because
tObservation x r since V r s O
dady
r cos 0 da ran so dor Tiz
z JEE d zJ r TO DOr z Iz theer J t
zdo e Iz O since
IZ
TIM z
Awesome
More generally EOEa o
c
Y x a sin O V alcos Of acosoI O Ie
4 a atom O V a see Of _a seal
OEOCE TEO
3 x a Sec O V altanOfatanlo
Conclusion If Such Square roots occur in
integrand we can do these trigonometric substitutions
to potentially get a trigonometric integral
Exampleda
o C TEO c 3Tzet x secco ddf tan co secco
doc tan O secco DD
J da J1
Tano sea 0 DOSECO tano
Jess DO sin O c must convertback to x
Clever Teich x Sec O ISCO
cos O x
AREsin V 70
IK
J doc c
more generally a
yx asin O since I 10
a2 x
Vatx a tomb tan x
a 10a
x asec O cos a11
a
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