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I am hoping for some help looking at the exponential function in Cartesian land.

If we are given $e^{-(x^2+y^2)}$ and asked to set this up over the domain of a disk of radius R both in polar and Cartesian coordinates, is this what polar would look like?

$$\int_0^{2\pi}\int_0^R e^{-(r^2)}rdrd\theta$$

In turn, is this what the Cartesian set-up would look like?

$$\int_{-R}^R\int_0^\sqrt{R-x^2} e^{-(x^2+y^2)} dydx$$

Any help or comments would be great. Thanks!

I am hoping for some help looking at the exponential function in Cartesian land.

If we are given $e^{-(x^2+y^2)}$ and asked to set this up over the domain of a disk of radius R both in polar and Cartesian coordinates, is this what polar would look like?

$$\int_0^{2\pi}\int_0^R e^{-(r^2)}rdrd\theta$$

In turn, is this what the Cartesian set-up would look like?

$$\int_{-R}^R\int_0^\sqrt{R-x^2} e^{-(x^2+y^2)} dydx$$

Any help or comments would be great. Thanks!

I am hoping for some help looking at the exponential function in Cartesian land.

If we are given $e^{-(x^2+y^2)}$ and asked to set this up over the domain of a disk of radius R both in polar and Cartesian coordinates, is this what polar would look like?

$$\int_0^{2\pi}\int_0^R e^{-(r^2)}rdrd\theta$$

In turn, is this what the Cartesian set-up would look like?

$$\int_{-R}^R\int_0^\sqrt{R-x^2} e^{-(x^2+y^2)} dydx$$

Any help or comments would be great. Thanks!

COMMENT - Thanks Gear Junky, that makes sense. I am struggling to remember to visualize the projection onto the xy plane. As far as evaluating it, I would definitely evaluate the polar coordinates. I was just practicing because he said we may have a problem like this on the quiz to set up in both but evaluate one.

I am hoping for some help looking at the exponential function in Cartesian land.

If we are given $e^{-(x^2+y^2)}$ and asked to set this up over the domain of a disk of radius R both in polar and Cartesian coordinates, is this what polar would look like?

$$\int_0^{2\pi}\int_0^R e^{-(r^2)}rdrd\theta$$

In turn, is this what the Cartesian set-up would look like?

$$\int_{-R}^R\int_0^\sqrt{R-x^2} e^{-(x^2+y^2)} dydx$$

Any help or comments would be great. Thanks!

COMMENT - Thanks Gear Junky, that makes sense. I am struggling to remember to visualize the projection onto the xy plane. As far as evaluating it, I would definitely evaluate the polar coordinates. I was just practicing because he said we may have a problem like this on the quiz to set up in both but evaluate one.