Trying to find a simple solution, there is a lot of info online, but I do not see what I need.
M = V*d
I have V, for instance, V = 3000
I have d as a function, for instance, 0.5(y + 3)(8 - y) in grams per cubic cm.
How to find a mass though integration, having a density as a function.
You have defined the total volume, but not specifically what volume of $3000$ you are interested in. The mass is $\int d dV$ Once you specify the limits of integration, the integral can be done (assuming they are simple enough). Contrast a volume near $y=5.5$ where the density is about $15$ with a volume near $y=8$ where the density is very small.