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Math Help - center of mass

  1. #1
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    center of mass

    Find Mx , My and (xbar,y bar) for the laminas of uniform density p bounded by the graphs of the equations.
    5. y= sqrt(x), y=x
    6. x= -y, x=2y, x= 0
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  2. #2
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    Quote Originally Posted by harry View Post
    5. y= sqrt(x), y=x
    M = \iint_D dA = \int_0^1 \int_x^{\sqrt{x}} dy \ dx = .1666

    M_x = \iint_D y \ dA = \int_0^1 \int_x^{\sqrt{x}} y \ dy\ dx = .0833

    M_y = \iint_D x \ dA = \int_0^1 \int_x^{\sqrt{x}} x\ dy \ dx = .0667

    \bar x = \frac{M_y}{M} = \frac{.0667}{.1666} = .4

    \bar y = \frac{M_x}{M} = \frac{.0833}{.1666} = .5
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