- #1

vanceEE

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px = t

t = s^2

$$ I = \int_0^∞ e^{-s^2}ds$$

$$I*I = \int_0^∞ e^{-s^2}ds * \int_0^∞ e^{-u^2}du = \int_0^∞\int_0^∞ e^{-(s^2+u^2)}du ds$$

$$s = rsin\theta $$

$$u = rcos\theta $$

$$r = s^2 + u^2 $$

$$ I*I = \int_0^∞\int_\alpha^\beta e^-{r^2}rdrd\theta$$

How can I find my limits of integration in polar coordinates?

t = s^2

$$ I = \int_0^∞ e^{-s^2}ds$$

$$I*I = \int_0^∞ e^{-s^2}ds * \int_0^∞ e^{-u^2}du = \int_0^∞\int_0^∞ e^{-(s^2+u^2)}du ds$$

$$s = rsin\theta $$

$$u = rcos\theta $$

$$r = s^2 + u^2 $$

$$ I*I = \int_0^∞\int_\alpha^\beta e^-{r^2}rdrd\theta$$

How can I find my limits of integration in polar coordinates?

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