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math_proof

  • 3 years ago

center of mass of the upper half(y>0 of the disk bounded by the circle x^2+y^2=4 with p(x,y)=1+y/2

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  1. math_proof
    • 3 years ago
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    is the integral \[\int\limits_{-2}^{2}\int\limits_{0}^{2+x} 1+\frac{ y }{ 2 }dydx\]

  2. philo1234
    • 3 years ago
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    Do the inner integral first.\[\int\limits_{0}^{2+x}1dy +\frac{ 1 }{ 2 } \int\limits_{0}^{2+x}ydy\] Do u know how to integrate?

  3. math_proof
    • 3 years ago
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    yeah

  4. math_proof
    • 3 years ago
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    how did you get that though?

  5. philo1234
    • 3 years ago
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    Properties of integration allows you to do this: \[\int\limits_{0}^{2+x}1+\frac{ y }{ 2 }dy = \int\limits_{0}^{2+x}1dy + \int\limits_{0}^{2+x}\frac{ y }{ 2 }dy\]

  6. philo1234
    • 3 years ago
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    Are u there?

  7. math_proof
    • 3 years ago
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    is that right what philo wrote? thats for My right? do i have to do it for Mx too?

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