As far as I know this has an analytical solution but I'm not sure how to go about doing it. Just to clarify, I'm not looking for a numerical method.
Sorry, don't know how to use maths symbols here:
I need to find x and y, such that the integral of exp(-ax^2 - b), evaluated from -infinity to x, equals 0.025, and the same integral evaluated from y to infinity equals 0.0975.
a and b are known constants.
(The question is just to find the 95% confidence interval from a posterior distribution).
Can anyone help?