Answer
$(\overline {x}, \overline {y})=(\dfrac{3}{5},\dfrac{1}{2} )$
Work Step by Step
We have $m_x=\int_{0}^{1} 12x (x) (x-x^2) dx=\dfrac{3}{5}$
and $\overline {x}=\dfrac{m_x}{m}=\dfrac{3}{5} $
Now, $m_x=\int_{0}^{1} 12x [(x+x^2)/2] (x-x^2) dx=[\dfrac{3x^4}{2}-x^6]_0^1=\dfrac{1}{2}$
and $\overline {x}=\dfrac{m_x}{m}=\dfrac{1}{2} $
So, $(\overline {x}, \overline {y})=(\dfrac{3}{5},\dfrac{1}{2} )$
