# Minimizing Resultant Volume

Calculus Level 5

Let $$a$$ and $$b$$ be real constants. Minimize the volume of the region bounded between $$y =x^2 + ax+b$$, $$x= 0$$ and $$x=1$$, when it is revolved about the $$x$$-axis.

If this volume can be expressed as $$\dfrac mn \pi$$, where $$m$$ and $$n$$ are coprime positive integers, submit your answer as $$m+n$$.

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