That looks like a variation on the "bell shaped curve", rotated around the x-axis. You can write it most easily as parametric equations using "x" and the angle of rotation as parameters:
Hello, I am trying to work out the function of this 3D object and it's parametrisation but after searching the web I have had no luck. Does anybody have any clue what it may be? I was thinking it could be some sort of inverse hyperboloid.
I am attempting to integrate this, do you know what the determinant of the Jacobian matrix would be?
You say that this is a variation of the bell shaped curve, is there a significant change or would it be ok to use those equations in finding the volume?