# Elimination of a parameter via Integration

Consider a function $P$ which integrates to unity in full space. $$P(a,b,c,d) = \exp\left[a^2 + b^2 + c^2 + d^2\right](a-b)(b-c)(c-d)$$ I need to eliminate $d$.

One way is to perform a linear transformation in which variables $a,b,c$ can be expressed in terms of $d$ and finally it can be integrated out. This is just a vague idea. I am really not sure if this will work and even if it does, I don't know how to proceed.

Also I would like to know if there is any other way to do this exercise.

• what do you mean eliminate? If $P$ is dependent on $d$, how can you remove this except by assuming some relationship $d$ has with the outside world? – gt6989b Apr 3 '17 at 16:58
• By eliminate I mean 'making Independent'. I want to make P independent of d. – NerdySnail Apr 3 '17 at 17:05
• Its full space. (sorry for incorporating physics terminology)@user251257 – NerdySnail Apr 3 '17 at 17:07