Centroid of the Region bounded by the functions: $y = x, x = \frac{64}{y^2}$, and $y = 8$.

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Can someone help and teach me how to solve this problem?

Find the centroid of the region bounded by the graphs of $$\begin{align} &y = x\\ &x = \frac{64}{y^2}\\ &y = 8 \end{align}$$

I'm having trouble solving this problem, please help. Thank you!

I currently don't know how to solve this problem, if someone would show a step-by-step solution would be very much appreciated!

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We can find the $x$ and $y$ coordianates of the centroid separately. There are several formulae that we can use: $$\sum m_i x_i=\bar x\sum m_i$$ $$\sum m_i y_i=\bar y\sum m_i$$ $$\bar x=\frac{\int_a^bxy ~dx}{\int_a^b y ~dx}$$ $$\bar y=\frac{\int_a^b\frac{1}{2}y^2dx}{\int_a^b y ~dx}$$ If that doesn't help, or if you have any questions, I will be happy to elaborate.