Can anyone help me with this integral $$I = \int_{a}^{\infty}t^2e^{-t^2} dt$$ $$I^2 = \int_{a}^{\infty}\int_{a}^{\infty}t^2h^2e^{-t^2-h^2} dt dh$$ Can you please explain how I can find the limits in the polar coordinates for the above integral? I am trying to do this similar to the way we evaluate the integral of Gauss distribution.
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1The use of polar coordinate is useful to calculate $\int_{-\infty}^{+\infty}{e^{-t^2}dt}$, not for calculating the integral from $a$. In your case, you don't need to use polar coordinates, just use integration by parts – Damien Nov 15 '20 at 11:47
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The Gaussian integral won't work here because of the different limits. See upper and lower incomplete gamma functions – K.defaoite Nov 15 '20 at 12:30