Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 years ago

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)

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  • 8 years ago
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    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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