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No. There are many functions that cannot be integrated.
All quadratic functions with real coefficients can be graphed on a standard x-y graph. Not all quadratic functions have real roots, maybe that's what you were thinking of?
If it is purely a Venn diagram problem then you cannot. Venn diagrams offer a way of solving certain types of problems graphically.
Beyond the fact that they are both measures derived from probability density functions, I cannot think of any similarity.