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I am to find the centroid of the area bounded by the curve $y=8x^3-24x+11$, the $x$-axis and the line $x=-1$.

Now I know that the centroid requires me to find the area under the curve first.

I have run into a snag in that this curve intercepts the $x$-axis on either side of $x=-1$ at:

$$x=\frac{-1-3\sqrt5}{4}$$ and $$x=\frac{1}{2}$$ My dilemma is whether I should integrate from $x=\frac{-1-3\sqrt5}{4}$ to $x=-1$ or start at $x=-1$ to $x=\frac{1}{2}$. I don't seem to find a specific rule to guide me.

Please help me out.

Martin Sleziak
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Medrine Nyamao
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1 Answers1

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This is just a clumsily stated problem. It is ambiguous. Either of those interpretations is as reasonable as the other. These problems are written by humans. They ought to do it better than that, but sometimes they don't.

Michael Hardy
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