Convert to cylindrical coordinates

  • Thread starter caliguy
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  • #1
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Evaluate by changing to cylindrical coordinates

[tex]\int[/tex] from 0 to 1 [tex]\int[/tex] from 0 to (1-y^2)^1/2 [tex]\int[/tex] from (x^2+y^2) to (x^2+y^2)^1/2 (xyz) dzdxdy

I came to an answer of integral from 0 to pi integral from 0 to 1 integral from r^2 to r (rcos[tex]\theta[/tex]rsin[tex]\theta[/tex]z) r dzdrd[tex]\theta[/tex]
Is this the correct answer?
 

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  • #2
LCKurtz
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Hello Caliguy. Click on the expression below to see how to post it so it is readable in tex:

[tex]\int_0^1 \int_0^{\sqrt{1-y^2}}\int_{x^2+y^2}^{\sqrt{x^2+y^2}}xyz\ dzdxdy[/tex]

This looks like a first octant integral. Check your [itex]\theta[/itex] limits.
 
  • #3
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To me they seem right, doesn't theta go from zero to pi? after graphing it it looks like a half a circle... maybe I'm overlooking something?
 
  • #4
LCKurtz
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Neither x nor y get negative in your original integrals.
 
  • #5
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So theta only goes from 0 to pi/2 right?
 
  • #6
LCKurtz
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