(5) A student used "U-substitution" 3 integral: S x² √√9- x² dx By using the following steps: Let U = 9-x² du = -2x dx - du 2xdx x² =√19-u substituting following ←つ answer: = 9-x² : =-12/20 · =√ S 2 - on the du √x.x²³ √ 9-x²³ dx X = S-² (9-~) u ²² 3/2 1/2 90²² - 0² qu du du After integrating and the student got the | 1 (9-x²15¹/²2 -3 (9-x² √²¹/²2 + c)

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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(5)
A student used
"U-Substitution"
the
Transcribed Image Text:(5) A student used "U-Substitution" the
5
A student used "U-Substitution"
integral: S x² √√9- x² dx
By using the following steps:
Let
U = 9-x²
du = -2x dx
- du zxdx
x² = 19-u
substituting
following
answer i
3
7
=
answer.
- du
S
x• x² √9-x² dx
1/2
= √5 - = (9-~) ~²
и
the
qu
1/2
U
3/2
9-x²
| 3 (9-x²)5¹/2² -3 (9-x²) ³/²2
du
After integrating and
the student got the
+C
du
3
Your job is to Redo S x² √9-x² dx
using Trigonometric Substitution and show you
get the
(show all steps).
Same
Transcribed Image Text:5 A student used "U-Substitution" integral: S x² √√9- x² dx By using the following steps: Let U = 9-x² du = -2x dx - du zxdx x² = 19-u substituting following answer i 3 7 = answer. - du S x• x² √9-x² dx 1/2 = √5 - = (9-~) ~² и the qu 1/2 U 3/2 9-x² | 3 (9-x²)5¹/2² -3 (9-x²) ³/²2 du After integrating and the student got the +C du 3 Your job is to Redo S x² √9-x² dx using Trigonometric Substitution and show you get the (show all steps). Same
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