Gaussian integral using polar coordinates

1. How do you express an integral in polar coordinates?
2. What is the integral of Gaussian function?

How do you express an integral in polar coordinates?

Use x=rcosθ,y=rsinθ, and dA=rdrdθ to convert an integral in rectangular coordinates to an integral in polar coordinates. Use r2=x2+y2 and θ=tan−1(yx) to convert an integral in polar coordinates to an integral in rectangular coordinates, if needed.

What is the integral of Gaussian function?

A Gaussian integral is essentially the area under the Gaussian function, between set limits along the horizontal axis.