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

*print*Print*list*Cite

Student Comments

aruv | Student

Area of the region between curves y=sin(x) and y=0 bounded by x=0 and x=pi

`Delta=int_0^pi(sin(x)-0)dx`

`=-(cos(x))_0^pi`

`=-[cos(pi)-cos(0)]`

`=2`

Let coordinate of centre of mass be `(barx,bary).` Then

`barx=(1/2)int_0^pix sin(x)dx`

`=(1/2){-xcos(x)+sin(x)}_0^pi`

`=pi/2`

`bary=(1/2)int_0^pi(1/2)sin^2(x)dx`

`=(1/8)int_0^pi(1-cos(2x))dx`

`=(1/8){x-sin(2x)/2}_0^pi`

`=pi/8`

Thus mass centre is `(pi/2,pi/8).`