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Math Help - expression in polar coordinates

  1. #1
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    expression in polar coordinates

    can someone express this in polar coordinates please


    \int_{-\infty }^{+\infty }\int_{-\infty }^{+\infty }\frac{dxdy}{(x^2+y^2+1)^{3/2}}
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  2. #2
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    Re: expression in polar coordinates

    Here you go:

    x^2+y^2=r^2

    \mathrm{d}x\cdot\mathrm{d}y=r\cdot\mathrm{d}\theta  \cdot\mathrm{d}r
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  3. #3
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    Re: expression in polar coordinates

    so is this the right one expression ?????

    \int_{0}^{\infty }\int_{0}^{\pi/2 }\frac{rd\vartheta dr}{(r^2+1)^{3/2}}
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  4. #4
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    Re: expression in polar coordinates

    so is this the right one expression ?????

    \int_{0}^{\infty }\int_{0}^{\pi/2 }\frac{rd\vartheta dr}{(r^2+1)^{3/2}}
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  5. #5
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    Re: expression in polar coordinates

    Quote Originally Posted by kotsos View Post
    so is this the right one expression ?????

    \int_{0}^{\infty }\int_{0}^{\pi/2 }\frac{rd\vartheta dr}{(r^2+1)^{3/2}}
    No, it is not. With \theta going from 0 to \pi/2, you are covering only the first quadrant. This would be correct if your original integrals had been from 0 to infinity.
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  6. #6
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    Re: expression in polar coordinates

    ok ...but what is the right expression to go on on this exercise please ???????
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  7. #7
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    Re: expression in polar coordinates

    An expression in which the range of \theta spans all four quadrants.
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  8. #8
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    Re: expression in polar coordinates

    And what is this expression ?Does anyone knows ?
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  9. #9
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    Re: expression in polar coordinates

    Quote Originally Posted by kotsos View Post
    And what is this expression ?Does anyone knows ?
    You have at least two possibilities: -\pi \le \theta <\pi and 0 \le \theta < 2 \pi...



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  10. #10
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    Re: expression in polar coordinates

    Quote Originally Posted by chisigma View Post
    You have at least two possibilities: -\pi \le \theta <\pi and 0 \le \theta < 2 \pi...



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