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
$\displaystyle M = \iint_D dA = \int_0^1 \int_x^{\sqrt{x}} dy \ dx = .1666$
$\displaystyle M_x = \iint_D y \ dA = \int_0^1 \int_x^{\sqrt{x}} y \ dy\ dx = .0833$
$\displaystyle M_y = \iint_D x \ dA = \int_0^1 \int_x^{\sqrt{x}} x\ dy \ dx = .0667$
$\displaystyle \bar x = \frac{M_y}{M} = \frac{.0667}{.1666} = .4$
$\displaystyle \bar y = \frac{M_x}{M} = \frac{.0833}{.1666} = .5$