Question

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

Answer 1

is the integral \[\int\limits_{-2}^{2}\int\limits_{0}^{2+x} 1+\frac{ y }{ 2 }dydx\]

Answer 2

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?

Answer 3

yeah

Answer 4

how did you get that though?

Answer 5

Properties of integration allows you to do this:
\[\int\limits_{0}^{2+x}1+\frac{ y }{ 2 }dy = \int\limits_{0}^{2+x}1dy + \int\limits_{0}^{2+x}\frac{ y }{ 2 }dy\]

Answer 6

Are u there?

Answer 7

is that right what philo wrote? thats for My right? do i have to do it for Mx too?