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Integration with Trigonometric Substitution

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janofano
#1
Mar2-08, 12:21 PM
P: 4
1. The problem statement, all variables and given/known data

Given integral (I):
I[(x)sqrt(9-x^2)dx]

by words:
Integral of "X" times square root of "9-X(squared)

Use proper trigonometric substitution to solve this problem.
2. Relevant equations



3. The attempt at a solution
Attached Thumbnails
integral_solved.JPG  
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rocomath
#2
Mar2-08, 12:29 PM
rocomath's Avatar
P: 1,755
You don't even need Trig substitution.

[tex]\int x\sqrt{9-x^2}dx[/tex]

[tex]u=9-x^2[/tex]
[tex]du=-2xdx \rightarrow xdx=-\frac 1 2 du[/tex]
janofano
#3
Mar2-08, 12:31 PM
P: 4
I know that I don't need that.
But the problem is, I have to use it.
The exercise require it.

rocomath
#4
Mar2-08, 01:21 PM
rocomath's Avatar
P: 1,755
Integration with Trigonometric Substitution

Well you posted the solution to it? I don't know what else to tell you. Just analyze what they did. Work it yourself a couple times if you have to.
Vid
#5
Mar2-08, 01:57 PM
P: 420
You forgot a term when you first did the substitution.

x = 3sin(u)
dx = 3cos(u)du

(9 - x^2)^(1/2) = 3cos(u)

So the integral becomes 27sin(u)cos^2(u)du
janofano
#6
Mar3-08, 02:58 PM
P: 4
[tex]\int x^2\sqrt{9-x^2}dx[/tex]
apropo
[tex]u=x^2\sqrt{9-x^2}dx[/tex]


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