Another Part where my brain's Fried

  • Thread starter Chaz706
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In summary, the conversation involves finding the integral of the expression \int \sqrt{4-x^2}^3 dx using the method of integration by parts and substitution. The conversation also includes a correction to a mistake made in the initial solution.
  • #1
Chaz706
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[tex] \int \sqrt{4-x^2}^3 dx [/tex]

I'm thinking integrating by parts would work, with u being that root and dv being dx, but is that the right method and direction. I've tried it and it seems more complicated.
 
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  • #2
Use [tex]x = 2 \sin \theta [/tex]...
then,
[tex]dx = 2 \cos \theta d\theta [/tex],
and your integral becomes:
[tex]16 \int \cos^4 \theta d\theta [/tex] .
Use [tex]\cos{2\theta} = 2\cos^2 \theta - 1 [/tex], etc...
 
  • #3
Damn it, no wonder I couldn't get it to work (I tried x = 2cos u)!
 
  • #4
So it's

[tex]\int \left(4-x^{2}\right)^{\frac{3}{2}} \ dx[/tex]

How about a substitution

[tex] x=2\sin t [/tex] ?

Daniel.

EDIT:Didn't see the other posts.
 
  • #5
x= 2cos(u) should work exactly like "x= 2 sin(u)": dx= -2 sin u du and
[tex]\sqrt{4- x^2}= \sqrt{4-4 cos^2(u)}= 2 sin(u)[/tex] so the integral becomes
[tex]-16\int sin^4(u) du[/tex] and the only difference is that "-".
 
  • #6
HallsofIvy said:
x= 2cos(u) should work exactly like "x= 2 sin(u)": dx= -2 sin u du and
[tex]\sqrt{4- x^2}= \sqrt{4-4 cos^2(u)}= 2 sin(u)[/tex] so the integral becomes
[tex]-16\int sin^4(u) du[/tex] and the only difference is that "-".

Oops, I made a slight mistake!
 
  • #7
Thanks once more! :)
 

1. What is "Another Part where my brain's Fried" about?

"Another Part where my brain's Fried" is a song by the band Stereolab. It is a track on their album "Dots and Loops" and explores themes of anxiety and confusion.

2. Who wrote "Another Part where my brain's Fried"?

"Another Part where my brain's Fried" was written by band members Tim Gane and Laetitia Sadier.

3. When was "Another Part where my brain's Fried" released?

"Another Part where my brain's Fried" was released in 1997 as part of the "Dots and Loops" album.

4. What genre is "Another Part where my brain's Fried"?

"Another Part where my brain's Fried" is considered to be in the genre of indie rock or experimental pop.

5. What is the meaning behind the lyrics of "Another Part where my brain's Fried"?

The lyrics of "Another Part where my brain's Fried" are open to interpretation, but they seem to touch on feelings of confusion and disorientation in the face of societal expectations and pressures. The song also seems to address the idea of mental exhaustion and the struggle to maintain a sense of self in a fast-paced world.

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