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# How do find the following center of mass in Calculus 2?

Find the center of mass of the homogeneous region in the first quadrant bounded by the curve x^4+y=1

I have the answer but I do not understand how to get there. (THANKS)

### 1 Answer

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- intc_escapeeLv 78 years agoFavorite Answer
M = ∫ ∫ dx dy

= ∫ 1 - x^4 dx [0,1]

= 4/5

My = ∫ ∫ x dx dy

= ∫ x (1 - x^4) dx [0,1]

= 1/3

Mx = ∫ ∫ y dx dy

= 1/2 ∫ (1 - x^4)^2 dx [0,1]

= 16/45

x-bar = My / M = (1/3) / (4/5) = 5/12

y-bar = Mx / M = (16/45) / (4/5) = 4/9

Answer: (5/12 , 4/9)

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