Integrate e^-x^2

Okay, this is more helpful. But it makes me wonder. When the function is transformed to polar coordinates, it becomes this:



r is just the function's position from zero. The volume of a cylinder is 2pi r h. Therefore, I could find the volume under the curve from r1 to r2, and since the volume of a cylinder is 2pi r h, I could divide to get the area underneath the curve?

I'm talking about applying this. How would I apply this to get the area under e^-x^2?

if you want the volume of a ring e^-r^2, for example 1 <= r <= 2, do 2 integrals. take the limits of one from 0 <= r <= 1 and the other as 0 <= r <= 2. subtract the result and integrate over theta (the r integrals give you the area under a slice of the sheet) to find the volume of the ring.

...im going to assume that you arent trying to find a volume with nonseparable limits like that nice mathematica picture you have there.