Use Trig Substitution. integral of x^2/sqrt 9-x^2.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 28E
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Use Trig Substitution.

integral of x^2/sqrt 9-x^2. 

 

dx
Case
9=3
U 3Sing
(3sino
9-(3sino)
du: 3C0s 8 do
• 3cos Odo
u=3SinO
Sin 0=e
9sin'O
,3cos odO
9-9sino
Sin'e:
=de
9sin 0
59(1-Sino)
3 cos odo
8=Sin'M
C 9sin o.
3 cosodo
Sin
C39sin O. 350d0
3co50
95in'e
Sin'g
9/3(-c05(26))
1- COS20
2.
Bin2o
2.
Transcribed Image Text:dx Case 9=3 U 3Sing (3sino 9-(3sino) du: 3C0s 8 do • 3cos Odo u=3SinO Sin 0=e 9sin'O ,3cos odO 9-9sino Sin'e: =de 9sin 0 59(1-Sino) 3 cos odo 8=Sin'M C 9sin o. 3 cosodo Sin C39sin O. 350d0 3co50 95in'e Sin'g 9/3(-c05(26)) 1- COS20 2. Bin2o 2.
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