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Math Help - polar coordinate

  1. #1
    Junior Member
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    polar coordinate

    Hi please, can you help me to solve this integral using polar coordinate
    Thank you

    <br />
\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} e^{-(x^2+y^2)}dxdy<br />
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  2. #2
    MHF Contributor
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    x^2+y^2=r^2

    Now you have e^{-r^2} which is the same as doing polar since you have x=rcos   and     y=rsin and squaring both removes the trig
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  3. #3
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    <br />
\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} e^{-(x^2+y^2)}dxdy=\int_{0}^{\infty} \int_{0}^{2\pi} e^{-r^2}r d \theta dr = 2\pi \int_0^{\infty} e^{-r^2}r dr = \pi [e^{-r^2}]_0^{\infty} = \pi<br /> <br />
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