Take notes so you can refer to this table: If the integral contains a? – x², try substituting æ = a sin 0. Then = a cos 0. do dæ If the integral contains a² + x² , try substituting æ = a tan 0. Then a sec² 0. %3D do dæ If the integral contains x² – a² , try substituting x = a sec 0. Then = a sec 0 tan ở do 1 According to the table, what substitution will we try for / dx ? 9+x² x = 3 sec 0, dr = 3 sec 0 · tan 0 OP x = 3 tan 0, dr = 3 sec? 0 . do x = 3 sin 0 da – 3 cos e 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 42E
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Complete Trig Substitution Table
Take notes so you can refer to this table:
dx
If the integral contains a? – x², try substituting æ = a sin 0. Then
do
а cos @.
da
If the integral contains a² + ² , try substituting x = a tan 0. Then
do
= a sec² 0.
If the integral contains x2 – a² , try substituting x = a sec 0. Then
dx
= a sec 0 tan 0.
do
According to the table, what substitution will we try for dx ?
9+x²
x = 3 sec 0
= 3 sec 0 · tan 0 .
de
x = 3 tan 0.
dr
= 3 sec² 0 .
de
x = 3 sin 0 ,
= 3 cos 0 .
de
Transcribed Image Text:Complete Trig Substitution Table Take notes so you can refer to this table: dx If the integral contains a? – x², try substituting æ = a sin 0. Then do а cos @. da If the integral contains a² + ² , try substituting x = a tan 0. Then do = a sec² 0. If the integral contains x2 – a² , try substituting x = a sec 0. Then dx = a sec 0 tan 0. do According to the table, what substitution will we try for dx ? 9+x² x = 3 sec 0 = 3 sec 0 · tan 0 . de x = 3 tan 0. dr = 3 sec² 0 . de x = 3 sin 0 , = 3 cos 0 . de
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