Find the center of mass of the region bounded by  between  and  above the axis.                     Thank You. 

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pramodpandey's profile pic

Posted on

Find the center of mass of the region bounded by y=sinx between x=0 and x=pi above the x-axis. 

`(barx ,bary) ` be coordinate fo centre of mass of the curve y=sinx ,betewen x=0 ,x=pi and y=0

`barx=(1/C)int_0^pixsinxdx`

`bary=barx=(1/C)int_0^pi(1/2)sin^2xdx`

`C=int_0^pisinxdx =(-cosx)_0^pi=1`

`I=int_0^pixsinxdx=(-xcos(x)+sin(x))_0^pi=pi`

`int_0^pisin^2xdx=int_0^pi(1-cos(2x))/2dx`

`=(1/2)(x-(1/2)sin(2x))_0^pi=pi/2`

 

``thus substituting these value in above equations, we have

`barx=pi ,bary=pi/4`  

thus coordinate of mass centre is

`(barx,bary)=(pi,pi/4)`

Rocky52's profile pic

Posted on

Sorry...

Find the center of mass of the region bounded by y=sinx between x=0 and x=pi above the x-axis. 

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